The cable that goes from the Power Button, down the side to the volume and hold buttons, then to the interconnect board has been torn/damaged. This requires replacement. There are 2 places where you can easily catch the cable and rip it. http://d3nevzfk7ii3be.cloudfront.net/igi... If you look closely here. You will see the cable go over the frame twice. I have made this mistake enough to not make it again.
Generally whenever I see this there are 2 possible solutions, once of which is not cool: 1) The LCD requires replacement (cross your fingers this works). 2) The motherboard in the phone has a bad fuse or something. This requires replacing the board/phone. Is the phone under warranty? If it is, then that is likely the easiest way to get it fixed/replaced.