Get a meter and start probing. If the reading is more than 5% off spec, the PSU is probably toast. You should check 3.3v, 5v, and 12v.
Next I'd reseat all power cables, data cables, RAM, video card, and monitor cable. Yes check the monitor cable, a loose cable can look like something died.
If the voltages is very close to normal and you don't see number fluctuating, and reseating everything doesn't help, it could be something else. That would leave the possibility of bad mobo, bad CPU, and bad video card. Can you hear any error beeps (if speaker is plugged in on mobo)?
I would suggest you get a POST diagnostic card to read the number and see if it reaches all the way to FF for normal boot or if it stops somewhere indicating hardware problem.