Ok, what you have is a fairly common brushless three phase hub motor. First some basics. The three fat wires that are yellow, green and blue are the three phase power wires from the controller to the motor. When the motor is running these will have what looks like alternating current on each, so you can't measure anything with a voltmeter by way of solving your problem.
The five thinner wires are sensor connections. Three of them (again coloured yellow, green and blue) are the outputs from Hall effect position sensors inside the motor. The red and black wires are the power to the sensors, usually around 5V (red is + black is -). The purpose of these sensors is to tell the controller the exact position of the rotor in the motor, so that it can keep the three phase AC in the phase wires in sync with the motor rotation. You can do some simple diagnostics on these sensor wires.
First, check that you have around +5V or so (it maybe anything up to maybe 8 or 9V, but 5V is typical) between the red and black wires at the motor. If you have, then that means that the controller is at least partially alive. Next, put the meter between the black wire and each of the three sensor outputs, the thin yellow, green and blue wires. If you power up and gently turn the motor you should see the voltage on each of these wires go high then low, then high again as the sensors switch. If all three sensors are switching, then the good news is that the motor looks as if it might be OK.
Next, check the motor with the controller disconnected, to see if the three phase wires (the thick yellow, green and blue wires) are OK. At the controller end of the motor cable, with your meter set to the resistance range, check between each of the wires in turn (yellow to green, green to blue, blue to yellow). Each should show a very low resistance if they are OK. If any show a very high resistance then the chances are you still have a broken wire somewhere. Next, to make sure that the phase wires aren't shorting to the motor case inside the axle, connect the meter to
each phase wire in turn and the case of the motor. You should see a very high resistance. Virtually zero resistance indicates a wire that's shorting.
Finally, with the power off and the battery and motor disconnected, and with the meter on the resistance range, check between each phase wire on the controller, as you did for the motor. The resistance should be high, if it's very low then you have a shorted FET in the controller.
Hopefully this will narrow down the possible fault. I gather you're in the UK, whereabouts? We have a few UK forum members, one of us might be near enough to help out.
Jeremy