LED's come on very dim, but fan won't spin. This means the voltage being output from the fan header is low - that's why the LED"S are very dim. With almost all fans, a very low voltage is NOT sufficient to start it up. That is why all fan controllers provide an initial FULL voltage for a few seconds, then reduce it to the desired setting. Your output is not doing that.
Your last comments just confirm that the maximum output of the connector is very low, and cannot be increased even when you tell it to do so. That fan output will never work unless you can replace the mobo components that have been damaged, which I do NOT suggest. Use another mobo Case Fan header - do NOT use the CPU_FAN or PWR_FAN connectors for this - or buy a manual fan speed controller that you can feed through a Molex 4-pin output connector from the main PSU.