HP proliant dl320 g6: all DIMM lights red, long beeping sound & internal health led red

I've seen this before and it's come down to the newer power supplies do not like the less expensive UPS systems.(it's not just HP) These new power supplies can detect fluctuation of 3ms and I've seen the UPS's response times to be from 3-5ms (on the low end). If you want to stay with Eaton try the PowerWare 9130

Well, you're trying to troubleshoot a circa 2006-2008 server that's fallen outside of its normal hardware warranty...

Internal health LED means just that. Internal health. Could be RAM, system board, CPU/CPU socket. You're also at the age where the system board battery could use a refresh. Nowhere in your post here did I see any indication of opening the server and reseating the components. Normally, that's the first step.

Now, outside of that, I recommended that you download the bootable HP Firmware DVD and run it on the system in your previous question. Did you do this?

If all else fails, you can call HP and talk to a tech. I don't know if you're in the US, so I won't post a direct number... but you can usually get fairly far in phone troubleshooting... but still, they'll ask you to update your firmware. So please do that first.

Edit:

You said that you received several of these old servers at the same time. Try swapping components or booting with a minimal set of components. One CPU, 1 or 2 DIMMs to start. And work up from there. At a certain point, though, how much is your time worth? This is a server that can be found for < $200US on the used market. If there's a problem with it, get a different one.