Apple laptop LCD screens are easily scratched due to close contact with the keyboard when they are closed. I have found a scratch remover that has helped me repair the damage caused by this keyboard/screen contact.

Background:
  I have purchased a few Apple laptop computers which had surface scratches on their LCD screens due to contact with the keyboard. One in particular was so distracting I wanted to do something about it.  I tried a product called Scratch Out made by Kit. I have used this product to remove scratches and scuff marks from my polycarbonate (Lexan) r/c car bodies with great results. It turned out to be a great polish for my PowerBook LCD screen as well.

Where Do I find Scratch Out?:
  Scratch Out is sold as a polish for car paint finishes and plastics. You should be able to find it at most retailers who sell other car care products.

How to use:
  Follow the simple directions on the back of the bottle. Remember to shake the bottle well and apply in a circular motion with a clean, soft, white cloth. Apply Scratch Out only to the areas you need to repair. Let the product dry to a haze and then wipe with another clean soft cloth.

Disclaimer:
  Most computer manufacturers will recommend you not use any type of product to clean your LCD screen for fear of damaging the plastic surface of the LCD. This is true if you are removing fingerprints, dust, etc.  For more information about how to clean a typical LCD screen search eBay guides for more information. This guide is offered to help those who have an LCD screen that is scratched and in need of more intensive cleaning/repair. Make sure you test Scratch Out in an inconspicuous place on your display to make sure it won't cause problems for your particular display. My experience using Scratch Out is with an Apple G4  Titanium PowerBook with a 15" display and 1 GHz PowerPC processor.

Best of luck on reviving your display...