my Hotpoint side by side has a dual valve solenoid. One for the ice maker and one for the water. They can fail independently. You push the water lever that in turn pushes on a switch that energizes the solenoid ( rod attached to something with a coil of wire around it - when energized it tries to throw the rod out of the coil; hence a movement that is used to open the valve and let water flow until the water lever is released then it closes. The opening in the valve is not very big and can get plugged up from particles in your water. If you have a well and do not have a filter this is most likely your problem. The solenoid is usually on the back side of the fridge sometimes tucked in behind a cardboard panel. Follow the water line to it...... push the lever and listen for the click. If it clicks and you get no water it is likely plugged up. If no click then there could be corrosion on the electrical contacts preventing it from operating or it could be burned out. I have torn one apart and cleaned it and it worked for a while but many are made such that if you cut it apart it is going to take a major effort to glue it back together. My appliance parts man says most problems with water or ice dispensers are with the valve......
Brooks - home handyman, September 2008