I use it in Prepar3D, which doesn't have Gremlins, and the problem is the same.

If I leave the aircraft sitting 10+ minutes with the APU running and the engines off, all the overhead annunciator lights remain lit and the battery indicates normal voltage, but the engines can not be started. Navigation lights are also off even though the switch is on, radios frequencies are not selectable. If I shut down the APU with this condition it will not restart Only restarting the sim resets the problem.

I have never been able to get ground power to work with the 737 or 727. It works fine with the 707 though, go figure...