That is a good observation. It goes a long way to explaining why nothing happens when the controller is in circuit (it should sense the voltage and cut out if too low to protect the batteries). It also explains why the motor goes from 0 to actually 50% when the battery is applied directly to it.
For me, the next step would be trying a proper 24v into the controller and seeing if it functions. Then you will know if you have to buy just two new batteries or batteries and controller.
Just a minor technical quibble: it is 'amp hour(s)' not amps per hour.
