Chances are good that the solenoid in the pump is either not activating (which engages the pump via the "ratchet" mechanism inside the pump housing), or the activation plunger is cracked and/or broken (it's nylon, I've seen NOS units with this thing broken from age). The star wheel runs with the motor when the wipers are on, current to the solenoid engages the pump, so get out the volt/ohmmeter and check for an open circuit in the solenoid coil, and if you have voltage to the coil when the switch is energized. Could be something as simple as the connector, broken wire, bad coil. Check the poppet valves in the plate, and also the condition of the piston and seals.
Regards,
Steve