On the CPU or the BIOS? I don't know what kind of chips the BIOS chips are, so I haven't looked up the spec sheets yet.
Anyway, I have a scope, but I haven't tried looking at anything yet.
Either, but if there's activity at the BIOS chips then there has to be activity at the CPU and you've verified the address bus and data lines.
The BIOS chips won't be flash, they'll be good old UV EPROM, probably 27C128 and I wouldn't rule out them having got corrupted over the years.
As you've got two of these boards pulling the BIOS ROMs from both board (label them so you know which came from which) could be a good way to check the contents, it's *highly* unlikely they'll both have gone corrupt in the same way so if they verify against each other then it's pretty likely they're good.
BIOS wasn't updated often on boards of that era because it was a pain to pull the chips, erase them, reprogram them, relabel them even if you could find a later or different version.
The 286 will be fed 5V direct from the PSU, they can get warm in normal use, more so if there's a problem somewhere so you need to know what those address and data lines look like.
Put your multimeter on continuity and check the ISA bus for shorts to GND or 5V.
You can use the same technique to quickly check for chip shorts on the TTL and chipset, just put one probe on GND and sweep the other down the chip legs, a quick look at the PCB traces and chip data shold tell you if you expect a short or if you've got a fault, again, you've got two boards so you can compare one to the other.
FWIW, I worked repairing PC boards like this, up to Pentium and yes, it's really nice to have elegant, thought out solutions and puzzle over the datasheets but the majority of boards were fixed with simple, unsophisticated techniques like checking for shorts, reseating, resoldering and visual inspection.