Sir HarveyCat . . . . . . .
What I am seeing on your last picture . . . . . is being the money shot.
On the bottom corner left is heavy RED cable that should be the 5 X 18650 battery packs + output
and the heavy BLACK cable which should be its - output.
The RED wire goes up to a power switch ? and comes out as a YELLOW wire and travels down to the board and connects to one of its pads and right between that pad and the lower pad that has the RED HOT motor wire connected to it is a white surface mount fuse F1.
Therefore you should thereby have a direct connection between the Battery + and the Motor + if the switch is turned on.
Confirm all of this with an ohmmeter and NO power connected.
Now, aspect two . . . . . .
To see if there is being a direct connection between the other battery wire, the heavy BLACK one earlier mentioned, and the path that it takes to a pad on the PCB and the other heavy black wire that connects into the motor.
If that circuit path is found open circuit, then, check the power device in a TO-220 black case, right beside them ( Pass on its ID #) to see if it has those 2 wires attached to 2 of its 3 terminals.
If so, you then have that situation of it probably being a POWER FET of a very low RDS on and in need of a weak gate turn on voltage to connect the two black wires via its Drain-Source conduction path.
On battery operated Power tools, that is being VERY VERY VERY common in their design and is used in the respect of disrupting a negative return line with one or two power FETS in order to stop operation in HEAVY overload conditions or the detection that you have finally depleted the battery charge condition, on down to its 2.5 V lower threshold of its cells.
Thaaaaaaaaaassit..
73's de Edd . . . . .
My favorite part of a marathon is watching the reaction of runners who reach out and grab one of my plastic cups of vodka.