If there's no rust or oxidization on the female pins inside the Molex, then it shoud be okay.
As far as the battery dying, I really do think you have a short.
Why?
Because , I've had MPU boards sitting on shelves for upwards of 15 years.
When installed in a machine, they retained the original CMOS settings and accounting.
They never shot out a low battery code [12] and were completely operational.
Mind you, not all were that good...some batteries were bloated like dead fish floating in the Hudson river in NYC.
Check the 3 fuses....are they all good?
They should be quick-blow fuses.
6A
8A
6A
Also check the legs of the three main eproms....GAME, REEL, and CMOS chips...especially the CMOS chip.
Make sure none of the small chip legs are folded underneath the chip body and are all straight into their respective socket holes.
This is where the bent screwdriver comes in handy.