Have you added any hardware to the computer from the original configuration? If your computer does not start up or if it does shut down all of a sudden without any warning; then it is possible that you have a power problem. Although power supplies are fairly inexpensive, you may want to try out a few other things first.
Do you have a UPS? No, I am not talking about an alternative US Mail service
Instead, it is a battery back-up; read: better then a power strip. You may want to look at getting one of these. It will not take care of your problem if it is your power supply, but it would at least assure that you are getting consistent power going to your computer.
Have you looked closely to your wires inside your computer? If any of your power leads are going out, or you see any scorch marks, it would show the same symptoms.
We are all curious like a cat. We wonder, we ask, we learn.
Please post back when a suggestion works, so that others may learn.