Scratched Discs

My Dark Souls magically appeared with 2 prominent scratches and 2 minor ones accompanying them when I took it out of my ps3 the other day. No idea how it happened, but it now refuses to load. 60% of the time it will show nothing when I load the game. About 45% it will just show the loading icon, but never reach the main screen. And one time it actually managed to make it to the main screen, I chose a build to play with, and then it stopped working.
I tried using the toothpaste method on the disc, followed all of the directions carefully, and the only result if any was more minor scratches.
I'm assuming I'll just need to get a new disc, my best friend even offered to get me one, unless this one is at all salvageable? Thoughts?

They can be buffed as long as the side with the graphics isn't scratched. Ps3 discs have DB extra protective layer on the other side and are supposed to be easier to recover than DVDs.

The clear side is the one that's scratched, and I wouldn't know how to go about buffing it outside of cloths, paper towel, toothpaste.

If you have a game store nearby a lot will do it for you for a couple bucks. If not there's inexpensive products available