It's almost certainly overheating - I see on average 8-10 of these each week - however clean your house ... a pc just attracts fluff ... and stores it in the heatsink
If you leave the box off for 5 mins ... does it startup ... then die again?
If it does ......
assuming we are talking about a reasonably modern PC ....
Open the box
Somewhere near the middle will be a
big lump of metal with a fan in top.
http://www.frostytech.com/articleview.cfm?arti cleID=902
What you need is a natural bristle brush
(one of the big fluffy blusher brushes is ideal)
GENTLY start to clean the fan ... getting right down into the fins of the heat-sink
Be careful ... if you rock the mounting you'll break the thermal contact and just make things worse
DO NOT use a vacuum. If you can't dislodge the fluff ... it's down to PC world to get a can of duster (yes really) It's compressed air and will safely blow away the muck
Certainly don't waste money on power units untill you do this.