After washing this board the issue still persists, even with the 5vsb and PS_ON resistor replaced with an 100k ohm (original was 0ohm)...
I get 1.84v on the fan power connector and 5v on the tachometer signal pin.
Any ideas?

I don't know what would be a typical cause for the board to be stuck in a Reset state. But I believe in always looking at voltages as a first step.

Use a multimeter (BIOS readings are unreliable) to check for voltages on the board, see if you find anything that looks weak or unsteady. Primary voltages from the PSU, battery, Vcore, and see if you can find DDR (spec is 2.5-2.7V for DDR400, 2.3-2.7V for older DDR), and anything else you think of.
I don't know what voltage the nForce2 chip uses, it might be the RAM voltage.

If all the voltages look good, then there's still the possibility of ripple caused by bad caps. Ripple is harder to measure and requires an oscilloscope.

If you have a good 12V on the board, but it's not getting to the fan headers, then you might have a blown transistor on the fan outputs. That tends to happen when excess current is drawn by an overpowered fan, or by a fan that has seized up.
Some boards have a separate transistor near each fan connector, and some have them shared.

The Asus A7N8X-series were insanely specific in their RAM requirements, failing to work correctly with many DIMMs that worked with no issues on other nForce2 boards. Not saying that is definitely the case here, but test with multiple DIMMs before assuming RAM isn't (one of the) cause(s)

After doing more testing, I found that the board gets hung up on memory error. I tested with some RAM sticks that worked with other KT400 chipsets, but none worked.

As for this weird behavior in the first post, once it is stuck in reset, once it isn't. I have confirmed that PS_ON and PWR button aren't shorted to GND prior to applying power. Already reflowed the weird SSOP16 Asus chip, but no go.

You've got a good CR2032 battery installed I assume?

It's possible you're still dealing with bad caps, even if they aren't visibly damaged or swollen.

They can create some really crazy problems, and the nature of caps charging\discharging means that the problems can be intermittent or seem to change when you do unrelated things.

Just a thought.

Oh... have you tried different power supplies? Preferably totally different models.