Wow, you guys are awesome, thanks for the help! The hairdryer (well, the heat gun) worked for me, leaving the power on (to check when the dispenser would work) and turning the temp control for the freezer to "off". Before I found this site and particularly, this thread, I wasted a lot of time troubleshooting, when Rich's suggestion up top would have told me if the water was making it to the freezer, and then the hair dryer method would have told me whether I had some mechanical issues. However, I started following the line from the wall out. I didn't mind running the line since I just bought this 25 year old house a few months ago and just love (sarcasm) to find the surprises in many of the electrical and plumbing installations. I prefer to find and fix now than find out when disaster strikes.
This started when I changed the filter on my GE Select and ran a full gallon and a half of water through the dispenser as per the manufacturer's (and GE's) instructions. I came back about two hours later - no water. I tried the filter I just replaced, but that wouldn't work either. I called the new filter company (Home Depot's HDX) and they instructed me to remove the filter and press the dispenser paddle a few times every fifteen minutes for a while to clear any excess pressure in the lines. The next day I called again and told them it didn't work. They said it could be my filter mount, and to call the fridge manufacturer.
Before I called anyone I did some troubleshooting. Since I had been able to dispense water when the filter was installed I knew it, the filter mount and the solenoid were all working properly. Also, when I pressed the dispenser paddle with the fridge door open I could hear the solenoid clicking. I started checking from the wall, and while it didn't help in this instance it sure helped in another! With the unit unplugged I removed the rear panel on the bottom (six bolts) and found the coils completely obstructed with dust. Even though when I moved in I pulled the fridge and cleaned the tile underneath, and vacuumed the louvers on the back panel, once inside I saw the coils were caked with dust (I found an exact example of the mess at http://friscorefrigeratorrepair.com/wp-c..., and please note this is not my photo). I'm so glad I opened that panel!
Anyway, the water flowed easily from the wall to the fridge intake, and from the filter to the quick connect behind the toe grill in the front. After time had passed I could tell the ice maker was refilling after dumping out the next load of ice. It had to be the line going to the water dispenser! I found terrifyingly difficult and/or expensive suggestions before I found this thread. Again, my thanks.