On my GE Profile refrigerator the water is controlled by a cluster of little solenoid operated valves at the lower left hand side as you face the backside. Whether you are asking for drinking water or your ice maker is asking for ice cube water, the primary water valve must supply the water in both cases. So, I don't think the primary valve is at fault since it works for ice making. Secondary valves direct the water to the ice maker or the water dispenser. I would guess that the secondary valve that directs the water to the dispenser could be at fault. Check its electrical connector. The system is more complicated that I imply but can be figured out by removing tubing from the valves one at a time and observing water flow when you push the dispenser lever, etc. (You'll need an assistant.) The tubes are released at the valves by pressing the ring at their connection toward the valve and pulling on the tubing. When replacing the tubing simply push it into the valve as far as it will go and pull it away again to seat the tube. It's fun to figure these things out. Draw a diagram as you discover things. Observe where each tube goes when it leaves the valve. Home Depot carries tubing and reusable couplers if you need to repair tubing.