I rented the same game from Blockbuster (or gamefly or where ever). Burn it to your hard drive on the 360. Then, put in your copy (the broken one). Launch the game from the hard drive. It works, you can take back the rented copy, and you can now play your game and instead of having to rebuy the game or anything, it costs you a few bucks. Its not pirating or stealing because you already own the game.
Obviously, if you can return it and get a new one, do that, but i had that problem with Rock Band 2 a few weeks ago and thats how i solved it.
Hope this helps someone, and if its been said or posted before, feel free to remove.
