Ice dispenser and water dispenser does not stop after use.

SOURCE: Kenmore Refrigerator stopped dispensing water

Either your water tank in the fridge froze up, the waterline that goes up the freezer door from the bottom hinge froze, or the switch that your glass hits is damaged. Do you hear any humming or noises when you put your glass up to get water?

SOURCE: GE Arctica (PSS26NGSB) ice and water dispenser

need to call ge at 1800-386-1215 some of these sxs have a door insulation issue that they will either send replacement doors to an authorized service company to exchange at no cost to you or offer a rebate for a newer model. yours might be in this group
have your model and serial number out of the ref located in the refrigerator section, about 4-5 inches from the celing down the right side and call and see

SOURCE: Water dispenser suddenly stoped working. Ice dispenser working

check the water line fron filter that continues on to water dispfrom icemaker, also a bad water disp solenoid or no pwr to water valve disp solenoid could be a problem,when you try to disp water can you hear a click from the solenoid operating to let water out?

SOURCE: Water dispenser not working. Ice dispenser works

There should be a water filter inside the water lines to the water spout. This filter could be clogged, or the water lines themselves may still be somewhat frozen and not allowing flow to the dispenser itself.
You can also test the power to the dispensor to make sure it is drawing water. Can you hear the pump trying to pump water to dispenser? The water valve should also be opening. You can test power to the valve that draws in water from the external water lines.

SOURCE: The water dispenser stopped dispensing.

At the bottom of the freezer door ( remove the kick plate ) , there will be a water line . Follow this line , about 6 " to a connector . Push in on the white ring and pull out the line , at the same time . Activate the water dispensor pad and see if water flows from the line under the refrig . If it does , then the line in the door is frozen . Either raise the freezer temp for several days , so the line in the door will thaw , turn on the dispensor light for several hours , or , I have heard using an air tank will blow the ice out of the line in the door . If no water comes from the line under the refrig , while activating the pad , then replace the water valve , behind the refrig , the piece the wall water line connects to on the refrig .
If the water line in the door is frozen , GE has a dispensor heater which comes with instructions to install . Pt # WR49X10173 .