Another thing that will pull a little more current is the fan motor. Even thou it turns without noise they sometimes get dry bushings and will eventually fail.
As 2oldman said, if you're dropping voltage through a extension cord, either remove it or get a larger one. Verify what voltage is at the post and then at the AC.
Have you checked run current to see what it is normally running at, when it's running "normally"?
There is a device to delay the unit from trying to start the compressor for a couple of minutes after power is applied or if the compressor cuts off. I would figure that would be part of the control board you've already replaced. It may not be. The item on some ACs is a separate device, one company that used to make them was Klixon.
