The disc is officially garbage. The 360 has a flaw, where if the 360 is tipped while running, it will permanently burn a damaging ring on the disc currently inside. It can't be recovered. This is not superficial, this is not dirt, and it is not something you can fix with a piece of cloth. And for the love of all that is holy, do not introduce a cleaning chemical into your machine.
Your choices are to either buy a new/used game from a retail store, or hit up Microsoft for their exchange program, which I think costs something around $20-$40 and only for Microsoft Studios published ones (I'm pretty sure Halo 3 is in that category).
*Edit*
Why the thumbs down?
my mom was being bad so grabbed my 360 an yank and whatever so she somehow scratched the disk without touching it...
1. Resurfacing the disc only works for cosmetic issues. I.E. the game cannot function due to inability to read the data behind the protective covering. You replace that film, hence 'resurfacing'.
2. You never, ever, ever introduce any kind of cleaning chemical, unless specifically made for use on an extremely delicate plastic surface (a disc cleaner). This cannot only permanently damage the disc you are attempting to clean, but it can also potentially destroy your machine via transference - damaging the same way it would the disc.
3. It was said, quite clearly, that the disc was damaged while inside the machine, due to someone yanking it. The 360's issue of destroying the data on the disc, not the covering or protective layer but the actual information on the disc itself, by tipping is very well known.
