You can do a basic "power on" test by jumping the green " Power_On" pin on the 24 pin main connector with any of the black grounds on the same connector.
I like to put a little load on the psu by connecting a fan or 2 before starting it.
This won't tell you if it's working in spec or not.
Then measure the main outputs:
12 volt - yellow to ground (black wire)
5 volt - red to ground
3.3 volt - orange toground
All should be +/- 5%
Then check the gray wire. If the PSU is on, it should be at 5 volts.
This is not foolproof because there is no load on the PSU, but if you cannot get these readings, the PSU is dead.