Sounds to me like the diaphragm might be shot. If you have already replaced the solenoid, and you are sure the wiring is correct, then troubleshoot the internals of the valve next. Shut off the water and remove the top of the valve. Pull the diaghragm and inspect for any excessive wear or damage. Clean out the valve, and replace with a new diaphragm if necessary. It could just be debris in the valve. You shouldn't have to replace the entire valve, very rarely do the bodies of valves go bad.
Tony Posey
Ridge Run Landscapes