I would disconnect the ATX power from the motherboard (both 20+4 and cpu +12v plugs) then do a standalone test of the power supply
View: https://www.youtube.com/watch?v=6vO4KnAeXE8
it's a good start - if that is good then might be good to swap your power and reset pins on the header and see if the reset can do the power on, although some cases don't have a reset button (please include what components & case you have will be helpful)
if nothing still, go bare-bones with the psu / cpu / mobo / 1 stick of ram and connect up your on-board IGP video if you have one (again would be helpful to list what components you have) and if not the GPU in question as well, plug in all the power and give it a go - sometimes just reseating the power and memory sometimes does the trick...