I think I am following you.
When the system regenerated it was drawing from the brine tank so maybe the rubber washer wouldn't be the problem here.
I should see the lower shaft start to rotate when I turn the star shaped dial. The fact that this isn't happening might point me in the direction of the drive motor.
If I took a multi-meter and tried to measure the output of the motor would that tell me anything about the motor? Since the motor only works for a few seconds it may be pretty hard to measure.
Thanks for your help with this.