There's no way to see your balance in your old wallet through private key or password.
You have to know the address to be able to check the balance.
So the best thing to do is finding your password. Try to check in a place or thing where you usually keep your passwords or important details. You can try to check in your old notebook in your old drawer. You can also try to check it in your browsing history if you didn't tried clearing it.
Private key doesn’t need password so if you are holding private key then you can have a direct access already to your wallet because you’re holding already the key. On this case was only the electrum backup or simply wallet.dat file is the OP holding which means this is an encrypted backup to access his balance. Private key is a different item from wallet.dat.
Nevertheless, the suggestion above is right on this case by brute forcing the password. But it might took a significant of time if the OP remembered password is different to the real password. This is the gamble on using brute force with a keyword set on it.
