How would I clean off a scratch off of my xbox 360 game

Well here's the story. I set my 360 next to my computer. I have a very short ethernet cable, so I have to share it with my computer. So that's why its next to my computer.

Anyways... I was done with xbox live for the moment, so I disconnect the ethernet cable, and put it back into my computer. Well I stupidly didn't realize that I was leaning over my 360, and it knocked the system over my keyboard. I picked it up, and the screen on my tv went black (the game was still on), and a few seconds later, it said on the screen "cannot read disk, try to clean it blah blah".

I open the tray, and take out my game (gh3). I look on the recording side of it, and it has a perfect circular scratch on it. I went "oh shit", and I started looking up websites to remove scratches. Well none of those methods worked.

Here's what I've tried:

*Rubbing plain toothpaste in a line back and forth, and then rinsing it under warm water.
*Same method as above, but with baking soda.
*Jewelry cleaner

Also, this is the forum that I think that it fits best in. Anyone who has a good method on cleaning my 360 game, thank you very much in advance!

 

Take it to a video rental place (blockbuster, family video, or similar)
they have pro machines they'll let you use for $2.00

 

Ive used these guys before.
http://www.skippydisc.com/

The come almost like new unless the scratches are really deep.