get a soft cloth some CD cleaner and a CD rotater the clean it
Bring it to your local game store and ask if they fix scratched disks.
tooth paste? are you kidding? you cant fix a game with tooth paste
put it in the freezer for 30 seconds then wipe it with a soft cloth
Your disc may be scratched, you can fix that by borrowing the game from a friend and install the game (from the game library tab) and then return it and it should work.
Blockbuster have a machine that will fix any scratched disc for £2, no matter how scratched, but it cannot be repaired if the disk is shattered or snapped and will have to be replaced.