It appears the female connector was re-pinned and has a new housing. If they didn't replace the male header pins that the connector plugs into, that could definitely be the cause. I can't tell 100% from the pic, but it looks like they may be original...i would unplug the connector with the red arrow and look at the male pins it plugs into. Do they look burnt or dull? As has been suggested here, the next step is to add those fuses for safety and rebuild the power supply board (which ultimately means replacing some capacitors and re-flowing solder joints for the most part)...

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Here's the section on pinwiki addressing the addition of 2 fuses for the backbox-mounted bridge rectifiers, one for the lamp bridge, one for the solenoid bridge. 8 amp slow-blow are the fuses they recommend using.

http://pinwiki.com/wiki/index.php?title=Williams_System_3_-_7#Additional_Fuses