Does putting toothpaste on a disc really help at all?

My Legend of Zelda Ocarina of Time is hopelessly scratched,but it only scratches and glitches (for however long you leave it on,it just stays glitched.And no Im not new to this) on Majoras mask,I don't know why.But my gamecube is breaking,its six years old,and so is this game,we got the special edition back in MI,and now its breaking.What can I do? I have used toothpaste,but that was for like 2 minutes,so i want to know if i leave it for 10 minutes will it help? and if not,the rubbing alcohol?