Whne you open your client, look in the bottom right and see if it has the HD logo at the bottom? If not there might be a problem in recovering your funds, also if there is and you added a password (after the backup) there might also be an issue recovering your funds. If you still have the old hard drive there are ways to restore the wallet file from that if it hasn't been overwritten but it'll probably be better to wait for it to sync to see if the funds are there.
(Ignore the part above about batch files, it's much faster to sync directly now for almost all cases).
I copied the wallet.dat file to an email last year, the file is only around 160 kb
Just for your awareness, please don't save these important things like your wallet.dat file over an email or cloud, you'll have full vulnerability of losing your BTC by getting your email hacked and wallet.dat file extracted as well as BTC stolen.
the hd logo is on the bitcoin core I just installed, but the screen says 0 btc even after I pasted my old wallet.dat to the folder, seems like I have to sync it first to find out, I don't remember if I added a password(very unlikely)
I'll sync it tomorrow and probably will find out in 5 days whether it's there, if there is a faster way to retrieve the fund let me know though
You'll have to sync it till the time of Blockchain when you stored them in that wallet and you're fine to check whether they're still there or not. Don't worry, they won't be gone if they're untouched and your email was fine during this whole year. To my knowledge, if your wallet is syncing then I believe you didn't set a password because it asks you one if you've put it and you're using an old password-protected wallet.dat file.
On a side note, don't you remember the address on which you had your coins? It's simple to check whether they're still there or not by visiting the BTC Blockchain explorer here -
https://www.blockchain.com/explorer and check with the address.