Battery Disabled - Inspiron 17R SE 7720 Windows 7

Windows 7 Home Premium 64 bit
BIOS: 01 Jun 2015 version (latest) 
Power adapter is a Dell OEM 240Watt FWCRC.   BIOS recognizes it as a 240W adapter.  The power port on the computer IS a bit loose and wiggly inside though. 

Upon startup, I get the dreaded messages about the battery not being recognized, or the battery being over temperature, depending on which battery I'm using

Approx 2 years ago, the weakening OEM battery was replaced with non-Dell replacement, which worked fine.  

I recently went to move the computer, so I unplugged it, and it died immediately.  After some investigation, I turned on the battery notification in the BIOS, and then started to receive this message with the non-Dellbattery:

Your battery is temporarily disabled. Please turn off your computer and try again when the unit is back to the operational temperature.

This is with a room-temperature battery, so I know there's no real temperature issue.

So I grabbed the OEM-Dell battery that has been sitting on a shelf, and installed it.  With the Dell battery, I receive this battery warning:

WARNING:  The battery cannot be identified.  The system will be unable to charge this battery.
Warning: The battery is not the recommended battery.  The system will unable to charge this battery.

So it doesn’t even recognize the OEM battery as a “real” battery.

Digging through the forums, I tried the “reset” sequence (and several variants) with no luck:
Turn off – remove battery - press/hold power button - restart without battery – login – shutdown – disconnect power – press/hold power button – install battery – restart

Is there anything that can be done at this point, aside from leaving it plugged in all the time?  

Yes, I'm aware that this is not a new computer, but is in perfect functional condition other than this issue.  Leaving it plugged in all the time is NOT a solution.

~Dave