Well the wallet let me send them, but the transaction hasn't gone through. I was trying to send them to hitBTC, any ideas?
You should not try to send them using the old wallet. It will not work. Try to do what
uralcryptocoin suggested:
You can run the old wallet and back up your private keys (you do not need to sync it just backup private keys) and try to import them to the new one
Will it work even though I've now sent them, or are they lost? is backing up private keys the same as backing up wallet.dat?
I don't think your coins were actually sent. In any case, you cannot lose them, they are either on your old address, or on your hitBTC account. As you did not get them on hitBTC, they are most obviously still on your old address.
Backing up the private kays is not exactly the same as backing up the wallet.dat. "wallet.dat" contains more than just private keys, it has its own format, and might fail to get recognized by new wallet if the format is changed somehow, but your private keys should work in any case.
To backup them, (1) run the old wallet; (2) open the console in "Help->Debug Window"; (3) run "listaddressgroupings" command and take note of all the addresses you have coins on; (4) get the private keys for every address with nonzero balance, by running "dumpprivkey ADDRESS" command; (5) save all the privkeys in a text file; (6) close the old wallet.
To restore the saved private keys, (1) open the new wallet; (2) wait for it to fully synchronize; (3) open the console in "Help->Debug Window"; (4) run "importprivkey PRIVKEY" command for every bucked up private key; (5) wait a bit for the wallet to rescan the chain to see your balance.