I bought my computer a few months ago and it was a prebuilt Lenovo desktop. I'm a big gamer so I also bought an nvidia gtx 650. I pretty much spent all my money on that, so I didn't have enough to purchase a new psu. It had been running fine on a 280W psu for a few months, then one morning I got up and there was no video output. I restarted it just to make sure, but then when I tried to turn it back on, it would only stay on for a few seconds, then shut off again. I tested the psu and it was faulty so I replaced it with a 585W one. After installing that I was still having the same problem so I took out the cpu and it finally would stay on. Does this mean that my cpu is fried or could it be a problem with the motherboard?
Well try disconnecting everything that is not required to boot your PC, so the DVD dive, floppy drive (if you have one), only have 1 stick of memory installed, disconnect the HD, and if you have onboard video then remove your video card too then see if it at least boots up so you can get in the bios.
After that you can start reconnecting your devices like DVD, HD, one by one.