So the CPU should be out of reset, but you're still not seeing any activity on its address lines? At that point I'm lost, I'm pretty certain that once Reset is released that the CPU should start fetching instructions, so low bit value address lines should be switching. Quick look at the 486 datasheet says there's also an Sreset pin which is similar to the Reset pin, so maybe something else is holding it in reset?
Snippet from the 386 datasheet:
2.10 RESET AND INITIALIZATION
When the processor is initialized or Reset the registers have the values shown in Table 2-7. The Intel386 DX will then start executing instructions near the top of physical memory, at location FFFFFFF0H. When the first InterSegment Jump or Call is executed, address lines A20-31 will drop low for CS-relative memory cycles, and the Intel386 DX will only execute instructions in the lower one megabyte of physical memory. This allows the system designer to use a ROM at the top of physical memory to initialize the system and take care of Resets.
So I think there should be something happening. Stumped. What does HOLDA look like? I think that can disconnect the CPU from the address bus.
Speaker sounds like one of those little piezo buttons often solder on to motherboard, so from what you've tested it should be fine. Just to check, it does have the 4 pin connector to go from pin 1-4 on the header?
[edit, partly because I got my HOLD and HLDA the wrong way around: I know some boards won't boot if there's no battery, so maybe try putting ~5v on the external battery connector and doing a CMOS clear with the jumper? Maybe something is somehow disabling the CPU if there's no CMOS battery. Seems unlikely. Pin 78 of the 82c206 is a Vcc pin, check the voltage there. That chip also has a HRQ pin, so it could affect the CPUs. Actually, since there is a datasheet for it, probably worth checking the Sysclk (pin 15), Osci (pin 75), Reset (should be same as CPU, pin 10)], HRQ (pin72). But I am just casing around at this point. Hey, at least I think I helped with the power LED.]