When you say "around" the screen, do you mean the bezel surround around the edge of the LCD, or do you mean various locations across the surface of the LCD screen itself?
If it's the LCD screen surface, this has specific optical properties, so the only thing I can think of that might be possibly successful is the stuff to repair scratches on LCD and DVD discs.
For the bezel, where these are injection moulded plastic with a surface finish like metallic silver or piano black, scratching through to the underlying plastic is tricky to dress up. Sometimes a plastic (eg PVC) paint such as used in crafts might help, but it will always look patched.
Nothing abrasive like a polish will help in either case, it will make it worse.
Edited by Platypus, 06 September 2010 - 08:37 PM.