[JohnnieB]

A fully charged 36V battery pack will read at lest 38.2V, so you battery pack is not charged. However, that should be enough to move the cart a few feet.

A reed switch doesn't look like a switch. See attached picture.
Since the solenoid is clicking, whatever is connecting battery pack voltage to the red wire that goes to J1 Pin-4, is working and not the source of the problem you have, so leave it alone.

You say you get 36.5V on the solenoid and controller, but not where on the solenoid or controller.
The solenoid has 2 large terminals and 2 small terminals.
The controller has 3 large terminals, 2 small terminals and 5 plugs containing a total of 25 Pins.

What is the voltage between the B- and A1 terminals on the controller when the pedal is pushed just far enough for the solenoid to click and no further?