Maybe you’ve tried this… have you swapped out the SD card from your extra BB to the one with the issue. May not be the ‘fix’, but easy to try.
Yessir. No joy. 
One more thing, was the actual mainswitch detached when you tried it with the external switch?
If the main switch is bad but still attached it will still influence the outcome, try pulling the connector of the main switch when trying the external switch. (the fault may also be in the circuitry behind the switch though)