Frank, 2 beeps = Motor hall sensor fault (or confirmation during motor phase calibration).
A broken throttle ground wire or a poor connection in the ground circuit could cause full throttle.
It's possible that the controller could still be fine, and the reason the rear motor didn't run using the GM controller might be due to different phase settings.
If it hasn't been overheated, it could just be that one or more of the hall sensors has failed, but unfortunately the minimotors don't like running in sensorless mode as you cannot manually start them spinning like direct drive motors.
If you disconnect the hall sensors wires from the controller, and swap 2 of the phase wires over, you might be able to make the wheel motor run backwards in sensorless mode by spinning the wheel backwards and applying some throttle. If it runs backwards, this could be an indication that the controller has not failed.
It might be worth checking that you still have ~5V between the red hall sensors supply wire and the black ground wire, and then try and check for voltage variation between each of the hall sensor signal wires (Green, Blue and Yellow) and ground (Black) while slowly turning the wheel backwards.
If just one sensor has stopped working I would say it's just a sensor problem. If all three have failed, then it could be the result of an excessively high voltage being sent from the controller instead of the nicely regulated 5V.
To check the windings, compare the resistance readings between the disconnected phase wires, all three readings should be similar.
(Green - Blue, Blue - Yellow and Yellow - Green)
I don't know what else to suggest other than rechecking all the obvious connections between the hub and the controller.
Alan