Per andy:
Am I on the right track?

The sequence of events is:
1. Turning on power supply switch causes 5Vsb to go to +5 volts.
2. Pressing power button on case causes PS_ON to go from +2.4 volts
down to +0.8 volts, turning on full power to the motherboard and
drives.

I *think* I'm at the bottom of it all now.

Seems like if there's a fault somewhere in the drives or other
devices it can prevent the mobo from telling the power supply to
turn on power to the mobo.

I didn't have the expertise to check for the +5 volts, but I got
it down to where if my data drive was connected the power supply
would not turn on when I pressed the case's Start button.

Disconnected the drive, mobo fired right up.

Took the problem drive to work, hooked it into my HP PC there...
HP booted up, but took a looooong time.... and the drive was not
visible, albeit spinning.
--
PeteCresswell