When you press the start button, what happens exactly? Nothing at all?
Have you checked the power? ;-)
Apart from that, it can be many things at fault. But first is the power supply unit (PSU). Does it have any smell? Also check the motherboard carefully if you can see anything blown up there, or you smell anything. (Of course, open up the case only if it doesn't mean you lose your warranty, if you are still in the period!)