Dave should check if there is any measurable impedance between the common and any of the segments in both polarities. They should all read above 100 mega-ohms if the LCD hasn't been damaged due to DC drive voltage. Otherwise, the LCD is actually damaged, however, the low impedance output of the MCU is strong enough to drive past the DC resistance, but now, a battery powered app will draw too much power.
@Dave, please do a proper ultra high impedance test from the common to the segments in both polarities when measuring with your meter & report back. Also, one other test which might be too late to test is if the LCD turns on black at the same critical voltage threshold as a fresh new or AC driven LCD.