On your motor, R2 doesn't seem to be connected to anything, there is nothing on pad H.
If all cables check out fine, it suggests there is a fault in the controller. Follow Nealh's advice for checking this. If there is a fault, you have to ask yourself, why?
In my experience, this motor will run a little bit noisy, but otherwise fine with all Hall cables disconnected using the Voilamart controller, so I would not assume the reason for the motor not running is down to the Hall sensors.
The other thing I have not mentioned, with Voilamart controllers, NEVER desconnect the Hall cable with the controller powered up. With early models it will blow the Hall sensing IC in the controller.
This happened to me, but I was fortunate to get a replacement controller for free under warranty.
You could use the controller from your other bike to test, but you could end up making both bikes unserviceable by blowing the controller in your good bike, so one of these from China may be a consideration, at the end of the day it doesnt cost much more than the PCB you are thinking of buying.
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I would want to be absolutely certain about shorts between the cables. That is why people here keep saying, make sure you are sure. Be sure to bend and twist things around when you test, all it needs to blow something is a momentary contact, that might occur only when the wire is moved.