The pinball game trouble-shooter in me is screaming "bad connector". In fact, that's what it sounds like. Sure, it COULD be something with the bus controller, BIOS, or software conflict, but I'm willing to bet that there's a bad pin on the ISA socket, or a loose solder joint on the underside... or maybe even a cut trace.
Most of us PC retro guys (myself included) are so caught up in drivers and IRQs that we don't think to check for the physical sources of electronic problems. Examine the pins on the ISA slot... clean them gently (I recommend cardstock, like an uncoated business card, and a little alcohol... slide it into the slot and check the paper- there'll probably be dirt on it). Use a flashlight and a magnifying glass and look into the slot itself too... all the pins should look the same. If one is bent or broken, that's the source of the trouble. Also check for solder joints near and around the isa slot that look like a surface-mount component might have broken off. Comparing that area to the other slots might show you there's a vital piece missing... sort of a "what's different about this picture" scenario.
Also flip the board over and examine the solder joints. Look for loose or off-color solder joints. If you are skilled with a solder iron, you can reheat them. Solder joints that take a lot of current sometimes "donut", that is, they remelt and form a donut around the pin on the edge of the hole, making little or no contact with the pin in the center. This happens in older arcade games sometimes, and I imagine could happen on a motherboard too. It's a 10-second fix if you know what you are doing.
Anyway, good luck. Maybe you'll find the source of the problem. Another rule of thumb, at least in pinball repair, if you see anything burnt, even if it's just a small shadow of a burn mark (or a blown capacitor -google that if you're interested), that's pretty much for sure your problem.
Glad you nailed it down to something! Good onya.