I just blew the dust off my Series One and yanked the battery. When I replaced it, I found that the LED on the face of the CPU module was off, but the 'Batt' LED on the face of the handheld programmer was on, and bit 377 was also on, just as you describe.
To reset bit 377, on the handheld, press 'SET', 'SHF', 3,7,7, 'ENT'
It appears that the LED on the CPU reflects voltage level, while the handheld monitors bit 377.