I have never heard of anyone getting a bad cpu, but I have heard of them receiving doa motherboards. Since it all turns on, but without display, I think they are both good.
How about more info. What board, what cpu..basically your whole computer specs
Try re-seating your RAM. I was working on my PC once and took the RAM out, when I booted the computer (with all the RAM in) I didn't get any display at all. Just took it out, wiped it, and put it back in and it worked fine.