It could also be the motor needs PWM control signal to operate.
Be careful, if inadvertently apply +V supply to PWM wire this could damage the control circuit in the motor.
When you finished playing with the motor...
Does your multimeter have Diode Test function? (most do nowdays), when you check the components I suggested we will know more what might be ok or need to replace.
The diode test applies a small current & displays the voltage of the circuit under test. It is great for revealing shorts, can see briefly ..uF capacitor charging, AB compare test etc...
The battery would have supplied most of the current to finish off D1 so T1 could be still ok.
D1 is not needed to run fan from battery, its part of the charge circuit, DON'T connect DC charger supply without D1 diode!, T1 is only a 30V device.
Have you checked/re-solder battery +pin solder join ? It looked like cracked solder in the photo.
As you mentioned earlier you have LED's so this shows logic supply N1 & MCU N2 are ok.