Will not dispence water

Either valve solenoid supplying water to ice maker is bad, or supply tube to ice maker is frozen(which is typically caused by leaky water valve), or ice maker is bad.

You have a dual water inlet valve where your water supply connects. One goes to the ice maker and the other goes to the water dispenser by way of the water reservoir you mentioned in the fridge.

Open the door and hold the door switch down and try the ice dispenser. Do you hear any thing.You should hear the ice door open and the augur motor turning to turn the augur which pushes the ice out the door. If the augur doesn't turn Take all the ice out of the bin and try. perhaps the motor is too weak or the augur is locked up. Take the bin out and try to see if the motor will turn with no load. The motor is behind the back cover where the bin sits. See if you get power to it using a voltmeter when you try the dispenser. If you are, probably bad motor. If not ,dispenser switch or solenoid is not working.

1. Disconnect the unit from the electrical
supply and wait for 3 to 4 hrs to get ice melted.
2. Pull out and unclip the drip tray on the ice
and water dispenser compartment.
3. Remove the screws from the ice and water
dispenser compartment front panel and
turn it over. The selector switch pack and
dispenser switches are now accessible for
testing.

The water line is frozen in the door .Turn on the dispenser light for several hours , or , use a hair dryer aimed up into the dispenser , or , use compressed air in the tube going up into the bottom of the door ( computer cleaning bottle with a small tube ) , or , air compressor hose at the bottom of the door tube , or , order GE dispenser heater kit pt # WR49X10173 ( it comes with instructions ) . After you get it working , turn up ( warmer ) the freezer temp only slightly .

you have a bad door seal. replacement is better than repair. warm moist air is getting in and the condensation is freezing.

the fill valve for the ice dispenser has gone bad there are two separate fill valves for the water dispencer and the ice maker

I have kenmore two door fridge. My icemaker is not working but the water dispenser is. Model#DU800DWGQ1 Serial#FJ1814737

check inside the bottom of the refrigerator for water, the water line goes thru the back of the refrigerator and it may have cracked and leaking inside instead of going to the dispenser. 
if not then water is most likely frozen in the line going thru the back of the refrigerator. look behind the pans in the refrigerator and there should be a coil of clear plastic water line, this is the reservoir that chills the water for the dispenser. sometimes it will freeze up if the refrigerator is very cold.

replace the dispenser control under the front panel on the freezer door if need detaild instuction after receiving parts reply to me

We had the same problem. Our frigerator is 1.5 year old. Everytime we try to dispence water or ice the dispencer clicks and the whole thing turns of. We had a GE repairman come by: the electronic board needs to be replaced: total cost $350. (cost of the board only: $150. We are considering disconnecting the dispencer by unplugging the board (according to the repain man the ice maker wil still work)or buy a new refrigurator (for sure NO GE!!!!!!)