Try disconnecting the PSU from the motherboard and all drives. Attach an old HDD to one of the 4-pin Molex connectors, so the PSU has some load on it. Connect mains cable to input and now short together pins 14 and 15 (this is for a 20-pin power connector) on the PSU. Pin 14 is usually green, pin 15 is black (ground). Drive should spin up and fan inside PSU should run whilst those wires are shorted. That at least will give an indication that the PSU is working, although it could conceivably still be faulty with a full load on it.
Two other things to try. Disconnect the mains power cord from the PSU. Connect up the leads to the motherboard, drives etc., and turn the mains switch ON at the back of the PSU (if it has one). Leave it like this for 10 minutes or so, to give the PSU's capacitors a chance to discharge. Now gently offer up the live mains power connector to the socket on the PSU. If power is running through the AC input stages of the PSU, you will hear a slight "crack" as the pins arc as you push in that connector. It's not a loud sound, but might just help prove if the PSU is faulty or not. The other thing to check is this. Do exactly as above, and when power connector is pushed in, watch the CPU fan to see if it momentarily moves just a fraction. If it does, then that suggests an overload of some sort, which is activating the crowbar protection circuit.
Let us know how you get on...
ROGER - G0AOZ.