The Power Supply is the first thing to check... check the psu fan through the rear of the case;
watch the psu fan as you push the power button.. if it doesn't run, the psu is bad...
if the fan does run, open the case and check the processor cooler fan. If it doesn't run, the following step is obviously to replace it.. If it does run check the processor heat sink is not lose on the processor allowing it to overheat. The processor overheats in just a few seconds if it is not cooled properly.
If all is right with the processor cooling, check the Ram modules are well seated on the slots.
After that check all power and digital connections are a tightly fitted on the hard drive and optical drives.