oh hell, I had this problem a while ago, I ended up buying a new overpowerful power supply, and then realized it was my motherboard that was wrong, this took me 3 months to figure out, I hope this is not the same problem as mine was. I have basically same setup as you from what you have told so far, apart from motherboard.

Here's a video from a while back of what my PC did, even after I had put in my new thermaltake toughpower 600W power supply, as you can see in the video - YouTube - Broken motherboard?