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On this GE refrigerator, the most common issue is that the water line inside the door freezes. Remove the kick panel below the refrigerator and freezer doors and look for the water line disconnect just behind the front panel near the freezer door hinge. Disconnect the water line and shut the door. Press the water dispenser and see if water comes out of the water line at the bottom where you'd disconnected the water line. If water comes out, you'll need to just turn the refrigerator off and leave the door open for about 45 minutes and that will allow the door to heat up enough that when you connect the water line to the door again, it should start to dispense water again. Using a hair dryer to warm up the door is also very useful.There is a kit designed to add a heater to the dispenser so this does not happen in the future if the problem comes back. Below is a link to the kit and it comes with instructions on how to install it.
Now if the water line is not frozen, that means your reservoir is likely frozen so thaw that out using a hair dryer for 30 minutes or so.
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