You cannot truly "fix" a scratched Xbox 360 disc. Scratches on the data side (bottom) permanently disrupt the laser's ability to read pits and lands. Commercial "repair" kits and DIY methods (toothpaste, banana, car wax) use abrasives that often worsen damage by creating micro-scratches or removing the protective lacquer.
Buy a used replacement. It's cheaper than resurfacing fees and guarantees functionality.
If the drive itself scratches discs (grinding noise, perfect circular scratches), the console needs repair or replacement.