Where are you located? Unless you use the heater, the aux pump should not be causing any problems. The aux pump is only triggered when you turn on the heater. It is designed to circulate coolant through heater core during heater operation. It is in no way used to assist during idle operation (stationary car). The name is somewhat misleading and people get confused about its actual purpose.
As for the electrical problem, first check you charging system. Next try connecting old pump (electrical plug only) to check if it spins (make sure the heater is on). I'm guessing that it doesn't work at all and that you have a load problem. Measure the voltage at plug (heater on) you should be getting battery voltage.
Measure the following as well:
1. Aux pump current draw (around 1.3 amp)
2. Monovalve resistance (11-19ohms)
If everything checks out you might have a problem with the pushbutton control unit.