Have you checked the batteries?
A lot of older machines used a pack of AA cells or a specialty oddball-voltage battery to back up the BIOS settings and the clock when the power is off. When the battery dies, the machine begins to report weird startup problems, as it discovers all the peripherals and settings anew every time it’s turned on. Modern systems generally use a button-style battery like you’d use in a watch.
Unfortunately, the size, shape, and style of batteries varies widely from one motherboard to the next. It can be difficult to find, test, and replace them. I had at least one machine that included a battery inside the clock chip - so the battery was not only completely camouflaged, it was actually soldered to the board. If that’s the case for your motherboard, it may actually be cheaper and easier to find another 486 motherboard than to replace the battery.
And of course, I could be completely wrong, or you might have thought of this already, or something. Good luck, though.