Yours is a Rev 3.1 there is also Rev 2.9 with either OD socket or PGA socket, and Rev 3.10 with Soc 3 plus other versions.....
No not having a battery on that era board should not prevent booting. Most common issue is jumpers set wrong or ram not compatible with board.
One other thing: if the cache is bad or cache jumpers are set wrong most older boards usually play dead....
Do you have a speaker you can attach and see if it beeps ?

Horun wrote on 2020-09-28, 00:50:

Yours is a Rev 3.1 there is also Rev 2.9 with either OD socket or PGA socket, and Rev 3.10 with Soc 3 plus other versions..... N […]
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Yours is a Rev 3.1 there is also Rev 2.9 with either OD socket or PGA socket, and Rev 3.10 with Soc 3 plus other versions.....
No not having a battery on that era board should not prevent booting. Most common issue is jumpers set wrong or ram not compatible with board.
One other thing: if the cache is bad or cache jumpers are set wrong most older boards usually play dead....
Do you have a speaker you can attach and see if it beeps ?

I believe I can hunt one up tomorrow. I did go through the jumpers for the CPU settings for the DX2-50 that's in the board now and they were OK; I didn't do a visual verify on the cache jumpers. I did see that it looks like the cache was upgraded at some point as the chips are two different manufacturers, so maybe they are off.

Updates:

Found a spare buzzer I was keeping for just this kind of thing - was getting what I would call '3 long beeps.'

According to a post I found on StackExchange, my issue very well may be that I only have 2 sticks of RAM in the board. From a reply on this page:

I see you have quite an early board with 30-pin SIMMs, which each provide 8 bits width to the data bus. Since the 486 is a 32-bit bus CPU (unlike the 386 it was never made in a 16-bit bus variant), you always need 4 identical SIMMs together. If you had a board that took 72-pin SIMMs, which have 32-bit width each, you'd be able to try just one like you are.

The effect of fitting just one SIMM in this machine would be to provide storage only at one out of every four bytes in sequence. Software just isn't written to cope with that on the PC.

I did get more in the mail the other day, but board is at work and additional RAM is at home. Hopefully they match close enough to the two that came with the board to be able to use as a set of 4. If not, I'll need to source matched quads of RAM.

*sigh*