EDIT: after loading up bitcoin core and doing a couple of google searches on some unfamiliar IPs I was previously connected to, I found that the number of connections have increased by a very large amount. It went from 6 to 4 to 56 connections.
That normally happens when you start a browser. It tends to connect to many things on the internet.
Have you tried doing a full resync? You can see if that will do anything before actually resyncing by renaming the datadir to something else and letting it make a new one. If it is able to establish connections, this means that something is corrupted in your block files, the block index, or the chainstate that is making it unable to connect, although I don't see anything in the log that indicates that that is happening.
Just tried that and still get the same error.
2017-08-31 00:36:05 Bitcoin version v0.14.2
2017-08-31 00:36:05 InitParameterInteraction: parameter interaction: -whitelistforcerelay=1 -> setting -whitelistrelay=1
2017-08-31 00:36:06 GUI: "registerShutdownBlockReason: Successfully registered: Bitcoin Core didn't yet exit safely..."
2017-08-31 00:36:06 Assuming ancestors of block 00000000000000000013176bf8d7dfeab4e1db31dc93bc311b436e82ab226b90 have valid signatures.
2017-08-31 00:36:08 RandAddSeedPerfmon: 230568 bytes
2017-08-31 00:36:08 Default data directory C:\Users\Laptop\AppData\Roaming\Bitcoin
2017-08-31 00:36:08 Using data directory F:\Bitcoin\Bitcoin\Data
2017-08-31 00:36:08 Using config file F:\Bitcoin\Bitcoin\Data\bitcoin.conf
2017-08-31 00:36:08 Using at most 125 automatic connections (2048 file descriptors available)
2017-08-31 00:36:08 Using 32 MiB out of 32 requested for signature cache, able to store 1048576 elements
2017-08-31 00:36:08 Using 2 threads for script verification
2017-08-31 00:36:08 Using BerkeleyDB version Berkeley DB 4.8.30: (April 9, 2010)
2017-08-31 00:36:08 scheduler thread start
2017-08-31 00:36:08 Using wallet wallet.dat
2017-08-31 00:36:08 init message: Verifying wallet...
2017-08-31 00:36:08 CDBEnv::Open: LogDir=F:\Bitcoin\Bitcoin\Data\database ErrorFile=F:\Bitcoin\Bitcoin\Data\db.log
2017-08-31 00:36:08 Bound to [::]:8333
2017-08-31 00:36:08 Bound to 0.0.0.0:8333
2017-08-31 00:36:08 Cache configuration:
2017-08-31 00:36:08 * Using 2.0MiB for block index database
2017-08-31 00:36:08 * Using 8.0MiB for chain state database
2017-08-31 00:36:08 * Using 1014.0MiB for in-memory UTXO set (plus up to 286.1MiB of unused mempool space)
2017-08-31 00:36:08 init message: Loading block index...
2017-08-31 00:36:08 Wiping LevelDB in F:\Bitcoin\Bitcoin\Data\blocks\index
2017-08-31 00:36:08 Opening LevelDB in F:\Bitcoin\Bitcoin\Data\blocks\index
2017-08-31 00:36:08 Opened LevelDB successfully
2017-08-31 00:36:08 Using obfuscation key for F:\Bitcoin\Bitcoin\Data\blocks\index: 0000000000000000
2017-08-31 00:36:08 Wiping LevelDB in F:\Bitcoin\Bitcoin\Data\chainstate
2017-08-31 00:36:08 Opening LevelDB in F:\Bitcoin\Bitcoin\Data\chainstate
2017-08-31 00:36:08 Opened LevelDB successfully
2017-08-31 00:36:08 Wrote new obfuscate key for F:\Bitcoin\Bitcoin\Data\chainstate: 11beca5e4f40da67
2017-08-31 00:36:08 Using obfuscation key for F:\Bitcoin\Bitcoin\Data\chainstate: 11beca5e4f40da67
2017-08-31 00:36:08 Initializing databases...
2017-08-31 00:36:08 init message: Verifying blocks...
2017-08-31 00:36:08 block index 67ms
2017-08-31 00:36:08 Reading estimates: 98 buckets counting confirms up to 25 blocks
2017-08-31 00:36:08 init message: Loading wallet...
2017-08-31 00:36:08 nFileVersion = 140200
2017-08-31 00:36:08 Keys: 102 plaintext, 0 encrypted, 102 w/ metadata, 102 total
2017-08-31 00:36:08 wallet 67ms
2017-08-31 00:36:08 setKeyPool.size() = 100
2017-08-31 00:36:08 mapWallet.size() = 0
2017-08-31 00:36:08 mapAddressBook.size() = 1
2017-08-31 00:36:08 Reindexing finished
2017-08-31 00:36:08 Initializing databases...
2017-08-31 00:36:08 Pre-allocating up to position 0x1000000 in blk00000.dat
2017-08-31 00:36:08 Committing 0 changed transactions (out of 0) to coin database...
2017-08-31 00:36:08 - Load block from disk: 1.00ms [0.00s]
2017-08-31 00:36:08 - Connect total: 1.00ms [0.00s]
2017-08-31 00:36:08 - Flush: 0.00ms [0.00s]
2017-08-31 00:36:08 - Writing chainstate: 0.00ms [0.00s]
2017-08-31 00:36:08 UpdateTip: new best=000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f height=0 version=0x00000001 log2_work=32.000022 tx=1 date='2009-01-03 18:15:05' progress=0.000000 cache=0.0MiB(0tx)
2017-08-31 00:36:08 - Connect postprocess: 2.00ms [0.00s]
2017-08-31 00:36:08 - Connect block: 4.00ms [0.00s]
2017-08-31 00:36:08 mapBlockIndex.size() = 1
2017-08-31 00:36:08 nBestHeight = 0
2017-08-31 00:36:08 Imported mempool transactions from disk: 0 successes, 0 failed, 0 expired
2017-08-31 00:36:08 torcontrol thread start
2017-08-31 00:36:08 upnp thread start
2017-08-31 00:36:08 init message: Loading addresses...
2017-08-31 00:36:08 Loaded 828 addresses from peers.dat 15ms
2017-08-31 00:36:08 init message: Loading banlist...
2017-08-31 00:36:08 Loaded 0 banned node ips/subnets from banlist.dat 2ms
2017-08-31 00:36:08 init message: Starting network threads...
2017-08-31 00:36:08 dnsseed thread start
2017-08-31 00:36:08 net thread start
2017-08-31 00:36:08 addcon thread start
2017-08-31 00:36:08 opencon thread start
2017-08-31 00:36:08 msghand thread start
2017-08-31 00:36:08 init message: Done loading
2017-08-31 00:36:08 GUI: initializeResult : Initialization result: 1
2017-08-31 00:36:08 GUI: Platform customization: "windows"
2017-08-31 00:36:08 GUI: "ReportInvalidCertificate: Payment server found an invalid certificate: " "01" ("Microsoft Authenticode(tm) Root Authority") () ()
2017-08-31 00:36:08 GUI: "ReportInvalidCertificate: Payment server found an invalid certificate: " "01" () () ("Copyright (c) 1997 Microsoft Corp.", "Microsoft Time Stamping Service Root", "Microsoft Corporation")
2017-08-31 00:36:08 GUI: "ReportInvalidCertificate: Payment server found an invalid certificate: " "4a:19:d2:38:8c:82:59:1c:a5:5d:73:5f:15:5d:dc:a3" () () ("NO LIABILITY ACCEPTED, (c)97 VeriSign, Inc.", "VeriSign Time Stamping Service Root", "VeriSign, Inc.")
2017-08-31 00:36:08 GUI: "ReportInvalidCertificate: Payment server found an invalid certificate: " "03:c7:8f:37:db:92:28:df:3c:bb:1a:ad:82:fa:67:10" () () ("VeriSign Commercial Software Publishers CA")
2017-08-31 00:36:08 GUI: PaymentServer::LoadRootCAs: Loaded 49 root certificates
2017-08-31 00:36:08 GUI: TransactionTablePriv::refreshWallet
2017-08-31 00:36:08 25: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 25: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 6: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 7: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 8: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 9: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 10: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 11: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 12: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 13: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 14: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 15: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 16: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 17: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 18: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 19: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 20: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 21: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 22: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 23: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 24: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 25: For conf success > 0.95 need feerate >: -1 from buckets 2.1e+015 - 2.1e+015 Cur Bucket stats nan% 0.0/(0.0+0 mempool)
2017-08-31 00:36:08 GUI: PaymentServer::initNetManager: No active proxy server found.
2017-08-31 00:36:08 trying connection 2.235.201.237:8333 lastseen=132.3hrs
2017-08-31 00:36:09 tor: Error connecting to Tor control socket
2017-08-31 00:36:09 tor: Not connected to Tor control port 127.0.0.1:9051, trying to reconnect
2017-08-31 00:36:11 tor: Error connecting to Tor control socket
2017-08-31 00:36:11 tor: Not connected to Tor control port 127.0.0.1:9051, trying to reconnect
2017-08-31 00:36:13 tor: Error connecting to Tor control socket
2017-08-31 00:36:13 tor: Not connected to Tor control port 127.0.0.1:9051, trying to reconnect
2017-08-31 00:36:13 connection to 2.235.201.237:8333 timeout
2017-08-31 00:36:14 trying connection 177.18.6.112:8333 lastseen=151.5hrs
2017-08-31 00:36:16 No valid UPnP IGDs found
2017-08-31 00:36:16 upnp thread exit
2017-08-31 00:36:17 tor: Error connecting to Tor control socket
2017-08-31 00:36:17 tor: Not connected to Tor control port 127.0.0.1:9051, trying to reconnect
2017-08-31 00:36:19 Loading addresses from DNS seeds (could take a while)
2017-08-31 00:36:19 connection to 177.18.6.112:8333 timeout
2017-08-31 00:36:19 Added 20 addresses from 8.8.8.8: 0 tried, 848 new
2017-08-31 00:36:19 Added 19 addresses from 104.28.18.99: 0 tried, 865 new
2017-08-31 00:36:19 Added 1 addresses from 138.201.55.219: 0 tried, 865 new
2017-08-31 00:36:19 93 addresses found from DNS seeds
2017-08-31 00:36:19 dnsseed thread exit
2017-08-31 00:36:19 trying connection 88.99.185.121:8333 lastseen=87.5hrs
2017-08-31 00:36:21 tor: Error connecting to Tor control socket
2017-08-31 00:36:21 tor: Not connected to Tor control port 127.0.0.1:9051, trying to reconnect
2017-08-31 00:36:24 connection to 88.99.185.121:8333 timeout
2017-08-31 00:36:25 trying connection 66.41.198.203:8333 lastseen=162.7hrs
2017-08-31 00:36:27 tor: Error connecting to Tor control socket
2017-08-31 00:36:27 tor: Not connected to Tor control port 127.0.0.1:9051, trying to reconnect
2017-08-31 00:36:30 connection to 66.41.198.203:8333 timeout
2017-08-31 00:36:30 trying connection 46.163.74.184:8333 lastseen=167.7hrs
2017-08-31 00:36:35 connection to 46.163.74.184:8333 timeout
2017-08-31 00:36:36 tor: Error connecting to Tor control socket
2017-08-31 00:36:36 tor: Not connected to Tor control port 127.0.0.1:9051, trying to reconnect
2017-08-31 00:36:36 trying connection 75.40.139.203:8333 lastseen=190.6hrs
2017-08-31 00:36:41 connection to 75.40.139.203:8333 timeout
2017-08-31 00:36:41 trying connection 88.99.36.224:8333 lastseen=168.4hrs
2017-08-31 00:36:46 connection to 88.99.36.224:8333 timeout
2017-08-31 00:36:47 trying connection 78.46.253.41:8333 lastseen=108.8hrs
2017-08-31 00:36:48 tor: Error connecting to Tor control socket
2017-08-31 00:36:48 tor: Not connected to Tor control port 127.0.0.1:9051, trying to reconnect
2017-08-31 00:36:52 connection to 78.46.253.41:8333 timeout
2017-08-31 00:36:52 trying connection 2.225.185.129:8333 lastseen=151.3hrs
2017-08-31 00:36:57 connection to 2.225.185.129:8333 timeout
2017-08-31 00:36:58 trying connection 82.72.88.33:8333 lastseen=168.1hrs
2017-08-31 00:37:03 connection to 82.72.88.33:8333 timeout
2017-08-31 00:37:03 trying connection 52.26.77.177:8333 lastseen=154.6hrs
2017-08-31 00:37:06 tor: Error connecting to Tor control socket
2017-08-31 00:37:06 tor: Not connected to Tor control port 127.0.0.1:9051, trying to reconnect
2017-08-31 00:37:08 connection to 52.26.77.177:8333 timeout
2017-08-31 00:37:09 trying connection 103.11.64.46:8333 lastseen=308.9hrs
2017-08-31 00:37:14 connection to 103.11.64.46:8333 timeout
2017-08-31 00:37:14 trying connection 45.56.99.96:8333 lastseen=318.1hrs
2017-08-31 00:37:19 connection to 45.56.99.96:8333 timeout
2017-08-31 00:37:20 trying connection 47.94.152.157:8333 lastseen=162.5hrs
2017-08-31 00:37:25 connection to 47.94.152.157:8333 timeout
2017-08-31 00:37:25 trying connection 199.34.127.173:8333 lastseen=151.9hrs
2017-08-31 00:37:30 connection to 199.34.127.173:8333 timeout
2017-08-31 00:37:31 trying connection 89.163.224.195:8333 lastseen=101.0hrs
2017-08-31 00:37:33 tor: Error connecting to Tor control socket
2017-08-31 00:37:33 tor: Not connected to Tor control port 127.0.0.1:9051, trying to reconnect
2017-08-31 00:37:36 connection to 89.163.224.195:8333 timeout
2017-08-31 00:37:36 trying connection 104.222.99.56:8333 lastseen=140.0hrs
2017-08-31 00:37:41 connection to 104.222.99.56:8333 timeout
2017-08-31 00:37:42 trying connection 35.195.79.250:8333 lastseen=91.2hrs
2017-08-31 00:37:47 connection to 35.195.79.250:8333 timeout
2017-08-31 00:37:47 trying connection 46.246.49.100:8333 lastseen=270.0hrs
2017-08-31 00:37:52 connection to 46.246.49.100:8333 timeout
2017-08-31 00:37:53 trying connection 188.234.245.16:8333 lastseen=291.3hrs
2017-08-31 00:37:58 connection to 188.234.245.16:8333 timeout
2017-08-31 00:37:58 trying connection 176.36.229.196:8333 lastseen=118.4hrs
This is another debug.log.
The client just keeps trying to find a peer indefinitely and I'm not sure this is supposed to happen.
It did produce a blk00000.dat file that is 16777216 bytes which is quite strange if there are no connections over the network?
I might try tommorrow to take my own piece of advice and see if booting it in safe mode does anything to fix the problem (if it does, then it's just my user account that's faulty).