There is a quick and easy way to tell if your power supply will turn on and it's called the paper clip test.
You take a paper clip and sperad it apart and thake the main motherboard power connector and insert one end of the paper clip into the green wire hole and the other end in the black wire hole and the psu fan should spin , if not it's not working.
While the paper clip trick will tell you if the PSU's fan is working, a working fan doesn't necessarily mean the PSU has the proper voltage on the rails. Your PSU may appear to be working, but not provide the correct voltage... especially when there is a load on the circuits.
I had the same thing , push the power button and the fan spins for a seond or two and stops. Take out the main connector and do the paperclip test and the same thing fan spins for a second or two then stops. By doing the paper clip test the fan is supposed to continue to spin if the psu is good . The end result for me was a bad psu because with the paper clip test the psu fan did not stay on.