Windex? Not just no, but hell no!
That will strip the oleophobic (anti-oil) coating on the screen.
The best suggestion that I have is to go into a consumer electronics store and find yourself an LCD/Plasma screen cleaning kit. These kits contain cleaning solutions that contain no alcohol or ammonia.
Endust makes one such product and the kit contains a microfiber cloth that will not scratch the screen. http://endustforelectronics.com/12275.php