Old ATX PSU: Could +5VSB have a minimum amps requirement?
When you just connect your ATX PSU to mains AC, no load, the +5VSB rail should be at +5V, and the PS_ON should be HIGH, either +5V, or +3.3V. 

You are saying that +5VSB  is normal (+5V and holds some load), but the voltage on PS_ON (green) wire is 0.7V. If the PS_ON is LOW (0.7V as you say) from the very beginning, the PS_ON circuitry is damaged/shorted, possibly by ESD. This pin has a simple pull-up, and must be shorted to ground to turn the PSU on. It is possible that, even when damaged, the remaining PS_ON circuitry needs a power toggling to turn the rest of PSU rails on. 

In modern ATX PSUs the PS_ON is managed by a separate specialized IC, and the PS_ON is a simple input, no other active components is there. If the pin is damaged, it can't be repaired, and only IC replacement can fix the problem.