If the game was only four days old, and you had the receipt, you should have been able to return it to the store for a new one. Just say that when you opened it it had the gouge and wouldn't play properly. They would have replaced it for a new one. However, now that you have smeared it with who knows what materials, it may be a bit harder to convince the store clerk.
I use a disk cleaner. It cleans disks.
To keep the system from ruining the disks, have it in a position where it will not 'tip over'. Take out disks after you are done playing and return them to their case. If you are running the console for reasons other than game use, be sure that a game is not in it. And, lastly, do not move the xbox around when in use.