Should have installed it to your hard drive first. Clean the disk, but don't play it, install it first. Also, try to have your 360 lying horizontal, not vertical (better air flow), and not on carpet. That should keep it from overheating. If the disk still doesn't work, maybe try installing w/ a rented version instead.
Does this happen only with this one particular game, or would it happen with all games?
Generally speaking, when the console won't read a game, it's an issue with the DVD drive. There are lots of tutorials out there on various fixes for it that I recommend finding and reading. Could be that the laser is not calibrated properly, problem with the magnet holding the disc down, dirty laser lens, etc.
