I read on this site that others have used part #WR49X10173 (water line heater) to remedy frequently freezing water lines for the dispenser. I called GE and this part is not compatible with this model (CFCP1NIYC - french door, freezer on the bottom, with internal water dispenser). GE said they would pay for parts if I had an authorized repair person order them, or I could have my frig replaced on a pro-rated program for an additional $1400. That didn't seem like a logical 'fix' to me so I set out to once again get the water line thawed.

What I ended up doing was this:
1. Remove the crisper drawers
2. Remove the cover of the internal water dispenser
3. Poke a weed-eater trimmer line into the tubing from the dispenser as far as it would go (it eventually went in farther as the ice thawed)
4. Fill 2 quart-sized freezer bags with very hot water and prop them up on the coils in the back of the frig (that are exposed when you remove the crisper drawers)
5. When hot water begins to cool, refill them and prop up again
6. Work the trimmer line in as far as you can
7. Remove the water filter, make sure it is not frozen up also (mine was not)
8. Engage the dispenser motor every few minutes, I started to hear the ice breaking up in the lines in about 10 minutes
9. When water begins to flow, remove the trimmer line and dispense a gallon or so to make sure the water is flowing well
10. Replace the dispenser cover and crisper drawers and remove the hot water bags

I know it can be a pain to do this but it is a cheap fix to get the water flowing again. Until GE designs a water line heater for the internal water dispensers that frequently freeze I'll repeat this when it freezes!

Hopefully this is helpful to others with Cafe refrigerators waiting for a re-design :)