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As far as I know the PSU has nothing to do with shutting down a PC. This operation is controlled by the MB.
Hope I am not breaking the rules by posting it Isolating ATX SMPS Supply and power related faults - PC Hardware Troubleshooting
My STANDBY (Purple #9 in the MOBO main power plug) is 1.74v "Should be 5v +/- 5%- If the standby voltage is not in spec or the led(s) are not lit, your PSU may be bad or the mobo may have a short.
Conclusion: Believe the PSU switching relay is shorted, and the MOBO ON SIGNAL (Green #14 in the MOBO power plug) is latched at 4.75v. Both are probably 'fried'.