According to HowStuffWorks, an unreadable CD, such as those used by the GameCube console, can potentially be fixed by using either a rubbing compound or toothpaste. Although neither technique is guaranteed to work, applying an automotive rubbing compound like car polish, or toothpaste to the back of a scratched, unreadable GameCube disc may render the disc functional again.
HowStuffWorks suggests dabbing a small amount of car polish solution onto the back of the scratched disc and then rubbing the compound all over the disc with a clean cloth, exerting some degree of force. Although suggestions as to the most effective polishing method vary, HowStuffWorks claims that there is little difference between rubbing in a circular motion and rubbing in a straight line from the center of the disc outward.
Toothpaste works similarly to car polish in repairing unreadable discs. Although the substance is not as powerful as car polish, it can often repair discs with only light scratches, and it is also cheaper and more commonly found around the house than car polish. Try using a plain white paste and avoiding more expensive gel-based products that contain extra ingredients. Apply a small drop of paste to the disc and use a finger to spread the paste outward from the center of the CD. Allow the paste to dry and then wash it off by rinsing the disc under running water.