Dear Nemanja,

How did you try to replace the wallet.dat?

This is what should actually be enough to work for you to be able to access your litecoins:

1. quit your litecoin client, make sure it doesn't run
2. navigate to your wallet's location. Windows: (%APPDATA%\Litecoin\   Example: C:\Users\UserName\AppData\Roaming\Litecoin
Mac:  ~/Library/Application Support/Litecoin/
3. replace only the wallet.dat in that folder with your old backup one
4. Launch the Litecoin Client, (perhaps check the wallet's addresses on block explorer to confirm before it finishes syncing) and wait for your wallet to sync