So, this is just a problem with the blower motor, then?
Do you have a volt meter to check for voltage on the dark blue wire at the motor?
OK, so the motor is getting power, so you are missing the ground.
If the motor is failing to run, even in the high position, then the heater control head is likely at fault.
You can remove the heater control panel and verify that it is properly grounded on the black/light green wire. If you have a good ground here and the motor won't run on high then the panel is faulty.
Yes, that does prove a good ground.
The black connector should have a grey/pink wire with battery voltage on it in the run position.
Those are all ground wires for the different fan speeds.
You can ground each of those wires to the black with light/green wire you tested earlier and this will provide a ground for each of the fan speeds........essentially bypassing the control head. If all works, then the control head is faulty.