OK, I measured the voltages on the PSU connector with
/PS_ON shorted to ground. ...
Everything else is within 2% of spec (3.3v reads 3.35,
12v reads 12.25, 5v reads 5.01 or 4.99).
Even defective power supplies can read 'good' voltages without a
load. Best load for testing is that motherboard.
-12 volts is ignored by voltage monitor circuits; would not cause
power supply cycling. And without some loading, -12 volts may read
incorrect (unstable) anyway. However -12 volts so far out of spec
could be a valuable symptom. We need more useful facts.
More relevant facts are necessary - numbers obtained by a meter. For
example, what does green wire voltage do when supply is power
cycling? IOW is supply cycling on its own or is it cycling because
power supply controller orders cycling? Green wire voltages would
report that necessary information.
Also important are voltages on any one of orange, red, purple, and
yellow wires. With a load, each must obtain minimum voltages of 3.23,
4.87, and 11.7 (numbers defined, in part, because of how meters
work). Purple wire voltage must meet specs even when computer is not
powered.
I suspect one of those voltages is on the low side or does not even
rise sufficient in first seconds after power switch is pressed. If
not, then gray wire voltage will not rise well above 2.4 volts within
seconds after power switch is pressed.
Numbers from these various measurements (without disconnecting
anything) will in but minutes either identify the failure or provide
information to provide useful replies. Disconnecting power supply from
motherboard (to jumper the green wire) simply does not provide useful
information other than 'power supply does start'. Even when on, it
could still be defective. No way to know without measuring voltages
under load - connected to motherboard.