Keeps disconnecting from xbox live when in loading screen?

Hmm, for the next step I'd try a router power cycle and check for any updates, in case there is a weird issue there. Past that, it's worth checking with MS support, they'd have more xbox-related steps.

Also, if you have a friend with a copy of the game, it might be worth swapping discs, in case there's damage. I don't think this is the case here, but if you can easily discount the possibility, it's worth doing so.