Svein, I think I've discovered why it did not run with the red and white wires connected. I've just tried connecting my battery with full throttle applied and nothing happens on mine either. If I then release the throttle and twist again, it works fine.
It would appear that the Pie's controller has a built in safety feature that prevents it from activating the motor if the power is turned on with full throttle applied, just like some of the speed controllers used on R/C Models.
Try disconnecting the red and white wires, turn on the battery first and then touch the red and white wires together
(with the wheel off the ground) and I think you'll find the motor will then run at maximum speed.
From your description, it definitely sounds like the throttle control is damaged, but I think you will be able to prove that the controller is still OK.
Give it a try and see what happens.
Alan