CPUs are both 5V and 33MHz FSB.

Well I went the opposite direction to you! I have this motherboard and went from 33MHz SX to a DX4 and then an AM5x86.

In order of least expensive and labour intensive fixes that I'd suggest:

*Are the CPU pins ok?
I would suggest making sure the CPU is aligned correctly as you certainly can put them in wrong but I can tell from the picture that it appears to be in the correct pins. I have found that with one of my boards, if a CPU had bent pins that were straightened out enough, it wouldn't POST yet it would work fine in another newer revision board that had a ZIF socket 3.

*Try another CPU
That looks like an early revision 486 as the original CPU in there from 1993 would have said "i486 DX™" under the white Intel logo. A quick Google search suggests this could be the earliest revision 33MHz part from 1990. Not that this should matter though. It's just a cool fact. I really doubt there would be an incompatibility although I've never used one of these and have no experience to talk about it. Maybe it's simply dead? Only another CPU can prove this.

*There is also a jumper on the board I think is labelled "UPGR" for CPU upgrade (without checking all three boards I have, I know it's on at least two of them) although seeing as you have an ODPR DX4 and no SX CPU soldered on, you shouldn't need to change this. Couldn't hurt to try though.

*The motherboard itself could be at fault.
This would be the last repair I'd try but from my experience, it was the problem with random CPUs not working on two out of three of my boards. On two of mine, the capacitors looked fine but over 50% had leaked slightly once I removed and could see them. Dell definitely cheaped out on these. My third board works fine and it's a spare so I haven't bothered to re-cap it yet but I suspect it's not too far behind the others. I had some really weird behaviour with mine. One would boot with an Intel 486DX 33, DX2 66 and an AM5x86 133MHz but not with a DX4 100. The other would boot only with a Cyrix DX2 66 and randomly the Am5x86. Never with an Intel DX, DX2 or DX4. Replacing the capacitors made every CPU work in both.

edit: truncated text during copy/paste

Thanks for the suggestions! I tried an SX-25 which worked ok and subsequently put the DX33 into a different (working) board - nothing 🙁
So it seems to be indeed the CPU (this is a first for me as I thought these old low MHz variants last forever). So I will fire up my soldering iron and find that thread about fixing a 486 CPU...😉

The oldest CPU I've ever seen fail (on its own and not from outside forces like power surges etc or excessive heat from negligence) was a Pentium 166. It simply got less and less stable yet never overheated. Glad it's going to be a cheap fix for you!

Well, I will look for another DX-33. Those overdrives are too much stress for such a venerable system...