Your description of the symptoms is a bit different than my one-time experience but Kenny Carpenter (now deceased, Bend Beaver expert) guided me to look under the transmission keypad into a black clamshell box for a couple of fuses, one of which had blown. He told me that to start the engine, the transmission must report neutral (N) on the keypad. The clamshell box is accessed by removing the large side panel under the console just left of the pilot's left leg.