Okay its simple. Your resistor is bad, 1 or more settings go bad..your high is a seperate relay built into the resistor thud why it works on just that setting... But your igniton switch is also bad.. Sounds like under load your accessory is dropping out. It's common and doesn't take too long to change either.
I can assure you it is definitely not your bcm.
Sent using my Galaxy SIII on Tapatalk 2