You could also try this:

Solution 3: Clear your system cache (game discs only)
If your Xbox 360 console can't play multiple game discs, try clearing your system cache. Here's how:

1. On the console, go to My Xbox, and then select System Settings.
2. Select Memory.
3. Highlight any storage device, and then press Y on your controller.
4. Select Clear System Cache.

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Select Clear System Cache


Note If Clear System Cache is not available, use the button sequence described in the following article:
971755 (http://support.microsoft.com/kb/971755/ ) How to clear the Xbox 360 console cache
5. Try to play a game disc.