RAM lights and fans and USB are 12v and 5v but that doesn't mean your 3.3v or negative rails are working.

https://www.lifewire.com/atx-24-pin-12v-power-supply-pinout-2624578

You want to simulate the motherboard by jumping the green wire to a common pin (I think - double check) 

Make sure all the pins in the Pinout are giving proper voltage.

This runs the PSU without any load, to help see if it's a PSU problem or not.

Sometimes PSUs won't give a rail, or it's out of tolerance, or it can kill your components.