Use ultra-fine sandpaper, buffing cloth and furniture polish to fix badly scratched PS3 games. Start with the sandpaper, and buff in circles to remove any deep scratches, which are typically only on the polycarbonate substrate level. Finish with a buffing cloth to shine the disc and a furniture polish to fill in remaining uneven lines.
When applying the furniture polish in the final step, do so in straight lines with a soft cloth from the middle towards the outside of the disc. Once it is properly rubbed-in and dried, use isopropyl alcohol to remove excess polish and properly clean and dry the disc. In cases where you do not have very fine sandpaper, toothpaste and a soft cloth are a suitable replacement.
If these steps do not work, check with a local used music, game or movie store, as they oftentimes have professional machines which do roughly the same process.