My First Mw2 game was torn up after my brother knocked my 360 over from its side to its wide side.

I bought a new game, and to prevent getting my games ripped up again, i installed the game onto my hard drive. The game will work fine for several hours, and then i'll always get these random "Disc is unreadable, i think this is kind of strange since i installed the game into my hard drive and the disc no longer has anything to do with it. The disc is completely unscratched, brand new. The xbox is about 4 months old.
What am i doing wrong? or How should/can i fix this problem?