K, so today a great idea came to me. Earlier, I posted that my disk was scratched and seemingly half-broken, but then I thought that if I rented another Fallout disk that worked and installed THAT onto my harddrive, and still used my old disk for playing, would the result be nearly the same condition of the game being played as it would on the working disk?
It would be the same result, but even better. Unluckily for me my Halo Reach disc was scratched beyond repair, I borrowed my friends and installed it, now the game works like a charm, and I don't have to hear the xbox go "click click click". So you should give it a shot, as it should work.
I think the disc just has to be able to be identified as Fallout New Vegas.