I used Meguires PlastX to fix my LCD cover. Its a plastic cleaner I picked up at walmart. Looks good as new now. Mine was pretty messed up but not as bad as yours. Worth a shot, good luck!
Plastic polish should get that off. Cover it with the same plastic stuff that people use for cell phones and ipods, the clear static cling stuff. WallyWorld sells it in large enough sheets back in electronics.