The fact that the board doesn't spit out beep codes even without RAM and the POST card showing "--" on the display confirms it's a pre-POST issue. Still cannot pinpoint with that what exactly the issue is, though. It could be a BIOS issue (though would have to be a completely dead chip or very corrupt BIOS for that to happen, which I think is unlikely), a power rail issue (rare - usually that would be caused by a bad MOSFET... which if it was the case, there would be a short-circuit or overload situation and the mobo+PSU will just show a "blip" of power before powering off), or some other hardware issue (mechanical issue with CPU socket BGA, burned out trace on an inner layer, etc.)
Seeing the state of the RESET line may indeed shed some light onto the issue... though tracing that could turn into a rabbit hole. As such, my preference is first to check the power rails on the motherboard to see if they are delivering the correct voltages. So that would be the CPU VRM low-side voltage (CPU V_core), memory V_DIMM voltage (2.5-2.6V for DDR or 1.8-2.1V for DDR2), memory V_TT termination voltage (about half of V_DIMM... so around 1.25V or 1.4-1.5V), CPU termination voltage, if any (don't remember if CPUs had it), Northbridge Vcc, Southbridge Vcc, AGP comm voltage, and Standby 3.3V.
Using the picture from TRW as a reference (this one)...
CPU VRM /V_core can be measured directly any any of the 4 toroidal inductors around the CPU socket.
RAM V_DIMM should be present on that toroidal inductor in the upper-right corner by the RAM slots
RAM V_TT should be present on that MOSFET-like IC with the 5 pins on the bottom (not sure which pin exactly, but one of them... be careful when you poke around there with your multimeter.)
Northbridge Vcc (or possibly CPU V_TT) can be measured on the toroid directly to the left of the Northbridge
The AGP comm/termination voltage is likely present on the tab or right-most pin on that large linear regulator at the upper-right corner of the PCI-E 16x slot
Southbridge Vcc should be on one of the pins on one of the SOT-223 regulators near (to the left) of the Southbridge IC
The standby 3.3 Vcc should be on one of the pins on the other SOT-223 regulator near of the Southbridge IC
I think that's about it with all of the voltage rails on this motherboard... or at least what I can tell from the pictures on TRW.
BTW, have you tried to see what happens when you connect your monitor to the onboard VGA? I know the chance of this is really small, but perhaps the POST card is not able to pickup POST cods for whatever reason *and* perhaps also the boards does not beep for successful POST by default (i.e. typically called something like "silent POST" in BIOS)... Yeah, I know, extremely small chance for this to be the case, but still worth trying perhaps, just in case.