EA Games has where you can use your EA Game account and redownload the game and apply your game key to it to play it like a clean install...
You should have an EA Games account or did you lose your account info? If you lost your account info you can regain access to it by contacting EA Games and proving ownership via credit card statement or ownership of registered e-mail account etc. Otherwise you have to buy a whole new copy of the game.
I ran into this issue a few years back with NFS Carbon that got corrupt on a system of mine, and required to be redownloaded and installed off the web. I had to prove ownership via showing e-mail address ownership and a copy of the transaction from credit card statement.
