Looking at the picture of the Motherboard, I can see you don't have all jumpers set for the DX4 CPU. I'm assuming the picture you posted is showing the jumper settings you've been trying.

EDIT: I've been staring at it for a while and I'm actually having a hard time figuring out the documentation.

Thanks for the help. Which jumpers do I not have set?

I tried to label the picture of the board per the documentation.

I agree, there are some things that seem odd in that manual but maybe this could help. Both Intel DX4 and AMD share many things similar but you did not specify which it is. Intel Dx4 (P24C) and most AMD DX4 use 3.45v, so set it to 3.45V and check the voltage on the heatsink/screw (to any ground) on the AS 2815AU you should see the same voltage as what you set the voltage jumpers. A DX2 5v will not be using that V reg but the DX4 3.45V will so if it does give 3.45v then the VRM could be the issue (OK I do not have the pinout to that Power Mosfet so it could be the left or right pin and not center). Another thing I see is that R17 SMT resistor right near it appears to be either burned or replaced as there is brown (burn or flux?) around it. The manual pictures you show are fairly poor in their description versus settings. I suggest for the DX4 you set JP16 : open. JP19: 1-2, JP20: open, JP24: open. The DX4 is an S cpu so JP14, 25, 26, 33: all closed like a 486DX2. JP15 and 17 : Open (even if a WB cache cpu it will boot set to WT).
edit: fixed one boo-boo, am sure I made others 🤣
Can you take a picture of the whole board ? And upload the manual here ? I looked thru TH99 and a few other sources but could not find anything that exactly matched.