Fan not working on motherboard even if same voltage works with batteries
Just a guess, but noctua do discuss Polarities.


  Polarity protection
  
  As many devices using 5V fans feature proprietary connectors and documentation of the pin alignment may not be available, the fan features an integrated diode for polarity protection. This way, you're on the safe side if you accidentally connect it with reverse polarity.


It would explain your observed:


  Current with fan mounted to the board, it is almost 0. I am assuming electricity is not going through my fan's circuit.