Thanks for the suggestions!
I ended up buying a new stick of RAM ($13 Amazon) and a new CMOS battery ($7 eBay) and replaced both.
No joy. Same beep code.
Pulled the RAM stick and got the "beeeep-beeeep, pause, beeeep-beeeep" for RAM missing.
It's got a RunCore SSD in it. I'm looking for the original SSD now to see if swapping that back in is the problem. Doubtful as I already pulled the RunCore and still same RAM related beeps.
Battery took a charge (eBay from a few years ago when it last worked). Pleasantly surprised there.
A real shame. This was my go-to quick machine for configuring new routers/APs/antennas.