So many crazy issue are caused by Gottlieb grounding that you can't rule it out, I would complete them. From your description of it's behavior being off and on I have to think you've got connector issues. I would complete grounds and then re-pin all the connectors and reflow header pins. I would not re-pin headers for now as for me anyway they are a pain but if your gremlins persist I'd do them as well.

You say it's been setting in pieces for ten years, was the battery left on the boards? If so you would do well to inspect it closely as acid damage usually spells the end, even if cleaned up and fixed it really only prolongs the death cycle.
Hopefully re-pinning, re-flowing, and the ground mods will eliminate all or at least most of your problems. After setting that long I'd check that all coils are loose and functionable, hell any thing that moves after that length of time.

Not reflowing edge connectors, you want to reflow the header pins and yes I always use a little flux as it seems to help liquify the old solder. I add a touch of new solder when reflowing, it helps with getting good joints, lessons the occurrence of cold joints etc..

You can re-tin the card edge pads on the board if they need it.