If your Xbox 360 is having disc read errors, there are several different things you can check to see where the problem might be.
1. Make sure your disc is clean. Fingerprints are the primary cause of disc read errors. To clean a disc, only use something 100% cotton that you’re sure is clean. Never wipe discs in a circular fashion, as this can drag dust or particles around the disc and cause scratches. Always wipe from the center out when cleaning a disc.
2. Try the disc in another Xbox 360 if possible to see if the disc is damaged.
3. Try to clear the Xbox 360 system cache.
4. Try to play the game with the hard drive removed, and with all memory modules removed.
If you continue to get disc read errors and you’re sure the disc is not the issue, you’ll probably want to submit a repair request through the Xbox 360 support site.