Use a volt meter to test the power supply. I'm pretty sure there's a thread here to show you how to do that. But it's pretty common sense if you know what you're doing.
But if you don't want to, just RMA everything back to Newegg. They'll take almost anything back without asking you any questions.
I've had that exact symptom before on one of my computers. Turns out, it was a bad motherboard, bad cpu, and bad psu. I started out by first RMA-ing the motherboard, then the power supply, then the CPU. Something must have fried everything in my computer.