I plugged in the Pelican Cobra TT Racing to my PS 2 (Cars Game) and the buttons and pedals work but not the steering motion. Help?

It could be the game not being compatible with the wheel, but it could be the wheel too. Ask the friend you got it from which games he played with it and see if you can borrow that game. Test it with that game to see if it works. If so, the Cars game is not compatible with the wheel. If this is not the case, the wheel is faulty. You can try to clean it by disassembling it and cleaning it from the inside, but many analog controllers can break pretty easily, and if that's the problem, the wheel is pretty much dead. I hope that the Cars game is not compatible.