How can I fix an Xbox 360 CD with a deep scratch for less than the game itself?

Anyways, I got mad at Burnout Paradise one day, and I turned my Xbox on it's side. Apparently the CD was pressed into the disc-reader, because the day I tried it again, a bit into loading it said "The disc is unreadable." Anyways, it's a very big and deep scratch, which goes all the way around the CD. Do I have to get a replacement, try to fix it with a lot of toothpaste and soap, or do I have to send it to Xbox or Criterion or EA?