So, thanks for all the advice.
Here's what did not work at all:
• Nail polish remover
• Windex
• Olive Oil (known to remove some sticky stuff, like pine sap)
• Painter's hand wash pre-moistened wipes
• iKlear Polish (didn't think this would work, but it's all I had)
Here's what worked only a little:
• vinegar and water (1:1 solution)
• rubbing with finger (got some of the upper sticky layer off)
• Zep degreaser spray (like Fantastic)
Here's what finally worked:
• Uni-Solve medical adhesive remover wipes
A friend of mine gave me a hospital version of this wipe (luckily she had one in her purse when I accidently bumped into her on my way to find a hardware store to buy Goo-off). The one wipe she gave me removed about 60-70% of the sticky substance. I searched around at Duane Reade and CVS, but neither store had these kind of wipes. Luck struck again when I came across a surgical pharmacy and they had a box of these Uni-Solves (the hospital brand is not available in stores). I bought the box for $17 for 50 wipes. Took only 2 wipes to completely clean the screen. I just had to keep rubbing, in circles, the trouble spots. I found out that I did not have to put too much pressure on the screen for these wipes to work; I just had to be persistent. Eventually, everything loosened up and I was able to remove the gunk with a micro fiber cloth. Everything is polished up now and looks as good as new.
The screen protector was from Griffin Tech. I called them and they told me to use lighter fluid. I was going to try the gunk-off stuff before I purchased lighter fluid because I don't like to keep that stuff around the house.
Also, none of the methods that I used above did any damage whatsoever to the screen. No scratches or discolorations or stains or anything. I have a 1st gen iPhone so I did not have to worry about getting the plastic back dulled by any of these chemicals, although I was very careful to keep the stuff on the screen alone. Also, the adhesive wipes that did the job contain alcohol, so the solution eventually evaporated.
So here's a pic of the removed screen protector. Look at the gunk! That was the same stuff that was on the iPhone screen. Actually, it looked worse on the iPhone screen.
So, thanks for everyone's help and support.
Antonio