Well in that case you can only look at the Power Supply, M'Board or CPU.
You'll need to inspect things and pay particular attention to the Electrolytic Capacitors near the CPU these look like tin cans standing on their ends. If any have bulged or are leaking the M'Board needs replacing. If they are intact then the most likely culprit is the Power Supply particularly if it is an unbranded one and finally the CPU.
If you have overclocked the CPU they will die soon rather than latter or if the heat sink has become detached they will die in seconds if that long. Also if the Heat sink Fan is no longer working or there is a buildup of muck in the veins of the Heat Sink it's quite likely that the CPU is now dead more so with AMD's but it can also happen with Intel's.
Provided that before this happened the case had remained closed it's unlikely to be a physically problem with the unit though I've seen some poorly assembled units where tie wire has been used and this has shorted out on the M'Board killing it.
You could also try reseating any plug in cards and push on the CMOS chip just to make sure that it hasn't part way worked its way out and is no longer making correct contact.
Col