Check the battery voltage at the battery terminals before and after plugging in. If the voltage goes up to 13.5 or better when you plug in, then your converter is doing its job. That means that you can not disconnect the batteries and still have power since the converter is on the battery side of the switch.
If the voltage does NOT go up, you have either a converter, fuse or connection problem between the converter and battery.
A multimeter is your friend.