COD world at war need tech help pls?

ok so i bought the game-the disc got broke-i wanted to reinstall it-so i download a torrent, the multiplayer works gr8-but when i click on singleplayer/co-op it says that it is the wrong disc, i am thinking about getting a no disc patch and installing another copy on my external hard drive but would that stop me from playing co-op?
 
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