Wouldn't alcohol destroy the finishes on the screen surface?
My container of anti-static monitor wipe, marked "safe for laptop and LCD screens", contains isopropyl alcohol. Most of them seem to be a 50/50 mix. The big thing in general is to use a very soft cloth. Normally, a soft cloth and distilled water is the best for cleaning things. In this case, assuming you have nothing to lose as the screen is already "damaged", I'd start at 50/50 and work my way up. Might also try adding in distilled white vinegar, but I would be careful about letting that solution get inside the laptop. As other have said, stay away from anything with ammonia in it.