I'm working on the same Frigidare FRS20ZRG for my sister and brother in law with a similiar problem - no water from the door but the icemaker works. All the lines seem open and clear so I suspect the Water Dispenser Valve Two and the I/M Water Dispenser Valve two assembly is the problem. The assembly is behind the cover on the lower rear of the 'fridge on the opposite side from where the water line attaches (that's the water valve one, by the way.) Your problem sounds like the inlet screen on the valve assembly is clogged. It's in the solenoid assembly behind the intake line comming from the first valve. You will see a nut on the line that unscrews to remove the line and gain access to the screen. Its in the hole where the line attaches to the assembly. If its not clogged, you can easily check the remaining lines by removing them from the assembly and blowing some air thru them. The solenoid plungers may also be sticking; mine were. They are easy to disassemble after removing the assembly from the fridge by loosening the one screw on the back and gently pulling the assembly out. Hope this helps, I will post more when I know more!
Rob Shelton
October 2005