Now the way you're gonna do this is first of all your going to unplug everything that goes from your power supply to your motherboard, so you don't dirty up the results at all. Once that's done, you're going to take a look at this. This is your ATX 12V connection, this is the main power connection from your power supply to the motherboard. The way we're going to do this is by taking a standard paperclip that we've bent out of shape, and we're going to put one end of the paperclip into the pin that's connecting to this green wire, and then we need another one that's leading to any of the black ones. So once we've bridged this connection that kind of tells the power supply that it's okay to turn on—if it's still functioning. So we know that if the power supply turns on, then it's working and that's not the problem. So what I'm going to do it put the paperclip right into this green lead, and then i'm going to connect it to one of the black ones as well.
Alright, once you have your paper clip in place what you need to do next is take your power supply power cable and just plug it back into your power supply. Make sure that if you have an on/off button on your power supply that it's set to the on position. Plug it in.
What you'll notice, if you've unplugged everything is that your power supply fan will turn on. I've left a couple of my blue LED fans plugged in so we'll be able to notice on the video, otherwise, my power supply is so quiet you wouldn't be able to hear it.
Anyway, so what I've been able to determine is that my power supply is working properly. If my case still wouldn't turn on once I've determined this then I'd know I'd need to start looking at my motherboard.
That's how you check a power supply with a paperclip. If your power supply is dead, shop for a new one here