Verified answer

It's possible that the power switch is faulty. Check around it and make sure nothing is hindering it. If the switch itself is bad, then I hope you are still under warranty.

Could be a heat problem with the CPU. Check to make sure the fan is going full force and if it is not then replace the fan . Compaq has a temp thing in it that will shut down the system if the cpu gets up to a certain temp.

its a ghost... check your power options under control panel