When you say that you re-pinned most of the connectors, I assume you mean the wiring harness side of them, correct? From experience, the power supply boards (well, ALL the original boards really) have problems with cracked solder connections on the male header pins. If you're taking the board out already, it wouldn't hurt to take a closer look... or even just resolder the 5v header if you have the tools/abilities. Don't just re-flow it, 30 year old solder doesn't do too well with the process, remove the old solder and apply fresh.
Now, you said the cap isn't on the board? the cap is wired in, and the wiring is sketchy? My honest opinion would be to get a proper 12,000uf radial cap and install it properly, and clean up the power wiring / boards of any improper repairs.
-Hans