I was wondering if the wallet.dat file that i use and is from 2014 is valid.
There is no reason your file shouln't be valid anymore.
Except maybe if your file is corrupted (error while copying / bit flipping / .. ).
I saw that if i put a new password on a wallet and the old wallet.dat file become invalid.
I'm not sure why the old wallet file should become invalid?
If you encrypt your wallet.dat with password X, make a backup and afterwards change your password to Y, then:
1) you will be able to decrypt your backed up wallet.dat with your password X
2) you will be able to open your newest wallet.dat with your newest password (Y in this case).
Will I be able to sync with this old wallet.dat file or is there a way I can check if it is valid or not?
Syncing with this wallet is possible, but not necessary. You can just decrypt this file and export your private keys to import them into another software. So no synching necessary.
Im not sure if there is a fast way to check if your file is valid (without decrypting it). Probably not.
I don't know which encryption algorithm core is using, but this file should (after encrypting) contain 'random' letter/numbers.