No scratches, laser burns, or cracks. Nothing. It isn't registered as a game in the disc tray.

Do other games register in the disk tray?

Yes, all but this one.

I would try cleaning the disk or try it in a friend's xbox.

If this happens to other games as well then I hate to tell you, but your xbox is nearing the end. This same thing happened to my brothers xbox and then it happened to mine as well. Consoles just die eventually....go get a xbox 250gb (aka SLIM) known to have less console failures.

If its only this game, try cleaning it...

Erm..not really. The Xbox360 was badly made from the start. I still have a Sega Master system, SNES, N64, Gamecube and PS2 that still all work perfectly. I know people who still have Atari 2600s that still work fine.
I love my Xbox360 but it's my second one. The first one broke in one year!