I just noticed this thread. Hopefully my input is still helpful. :/

The circles could be laser burns. They go around the outside of the disc? My brother smurfed up my copy of Reach by setting the Xbox right side up from laying down while it was playing the game. It got two laser burns around the outside of the disc and the game wouldn't load past the opening cutscene.

If that's what it is then the game is toast. You could try to get it fixed (what do they do, grind it?) at a Hastings or someplace but the chances of it working afterward are slim. But that's only if you moved the system while the disc was spinning. If not then it could be a multitude of things.