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There isn't a pin on serial for power or "negative". There is a grounding pin, but no dedicated power output. I'd wager a guess that it might have had more usage than merely providing additional power. Finding out what pins those wires go to would shed light on the problem.
Battery-backed SRAM uses a diode "wired-OR" scheme with a resistor on the battery node to give preference to supply current. The voltage isn't critical as state is retained w/ anything above 2V or so (1.2V + 0.7V diode drop) into the diode. Of course the SRAM itself won't like anything above 5.5V however. Wat about serial??? The data interface is Centronics parallel port. You actually CAN use serial port handshake signals as a low-current supply (as all mouses did at one time), but at ~13V you need to regulate it for electronics. If I were to go by the pics alone I wouldn't think it connects to a serial port or the DE-9 would be female and there would be a regulator. Perhaps it's on the board? Also it kinda seems stupid to be tethered to a serial port for backup when the whole point is to be able to bring the board away from your workstation.