Well, As the question you've asked, if it has FAILED, then it's junk...... or if you want to find out where it is going wrong there are a number of tools, (HARDWARE) available to test a PSU, the simplest one is I think from and electricians point of view a Multi meter, but if that's too complicated for you, you can try something of this sort,
There's two kinds of PSU testers (well, three if you count the DMM); the LED testers and the ones with a voltage display. The problem with the LED tester is that a dead PSU output gives the same indication as an output that is just a little out of tolerance.
To check the PSU with a digital multimeter (positive lead to PSU pin, negative lead to a black wire):
Yellow wires should be 12 volts. Red wires: +5 volts, orange wires: +3.3 volts, blue wire : -12 volts, violet wire: 5 volts always on. The gray wire is really important. It should go from 0 to +5 volts when you turn the PSU on with the case switch. CPU needs this signal to boot.
You can turn on the PSU by completely disconnecting the PSU and using a paperclip or jumper wire to short the green wire to one of the neighboring black wires.
This checks the PSU under no load conditions, so it is not completely reliable. But if it can not pass this, it is dead. Then repeat the checks with the PSU plugged into the computer to put a load on the PSU.