Try installing disc 1 on a USB or external hard drive. If that still doesn't fix it, it's the game, not you or your hard drive.
I'm guessing you have an original model 360? That's what I have, and along with many others we've found that the game doesn't work on these consoles for whatever reason. Just won't work at all. Need to wait on Rockstar to address the issue and stop ignoring it.