Long time lurker here... I got the dreaded "rainbow" rectangle on my screen that meant that the digitizer stopped working. I was pretty sad to say the least. I called Verizon and they wanted $95 to send me a new one with the silly insurance plan. I scouted google and saw that many other have had this issue.
So, I broke down and bought the replacement digitizer on eBay. Well tonight, as I looked at my broken phone, I thought that since I was going to be eventually replacing the digitizer, it couldn't hurt to try to mess with it a little. I noticed that the rectangle appears as a thin film between the top and bottom layers of the digitizer. This thin film is what causes the rainbow effect, just like a thin film of oil on top of water.
What got me thinking was that I had just set the screen to beep when tapped, and every time I turned it on it tapped once. This meant that the screen was actually being pressed continually. So, I thought that I'd try to pull the screen away from the bottom a little. I finally got some duct tape (of the clear variety), and carefully laid it over the entire screen. Then, I pulled off at a pretty shallow angle so it would pull on the top layer pretty good.
Well, lo and behold, the screen started working again! And there isn't a hint of rainbow/oilness at all. And it is totally responsive, as before.
So, if you are in the same boat, try some duct tape or similar.
Cheers!
acmegeek