There are several possibilities.
1) the controller is set up so it has to have Hall sensors connected. But I think this is unlikely as it is a dual mode controller.
2) the controller is not switching on, or it is not giving an output for some reason.
3) there is actually a break somewhere in the main wiring to the motor windings. Looking at your photos, it's hard to see that you have done the continuity test all the way from the 3 controller power cables to the motor windings, the insulation at those points looks intact.
Debugging this sort of thing is very frustrating process, hang on in there