For the motor to run (even intermittently as in your case) it requires an external voltage pulse. From schematics I reviewed, there is a + wire that goes to the motor control you show (#4 or the 2nd from the left) so if there is enough conductive dirt
in that connector and your picture does show a very dirty motor connector, then maybe it would operate. So, clean that motor housing and connector with varsol or some parts cleaner to get the grime off.
I would still try washing the circuit board with iso, I do not see why it would be of "no use" as you did go to all the trouble of removing the motor. I do see where there may be burnt electronic parts, but until you try....