haven't read all the responses but I'm going with one of two things
1) PSU - PSUs are the #1 (by far) reason for a PC to die. They are also the #1 overspec'd item in most PCs (hey, why sell a sufficient 500W supply when you can sell a 800W supply for a lot more and all the gamers think they need it). They fail the most often and cause all sorts of weird problems that aren't really explainable. My PSU failed once, which convinced myself and the tech support to think it was the mobo. Replacing the mobo did nothing and it was really the PSU which fried 2 mobos. If you have a spare one, swap it out to check.
2) Graphics Card - This is my second guess and the one I'm more leaning toward due to the lines on the screen. I had one die and I couldn't figure out what was wrong with the PC. Similar no video output. I had to reset the mobo and put a new graphics card in and then it finally booted up properly.