I have a 7 year old HP, P4 desktop running xp, that this evening when I have tried to turn it on, has started up but then the extreme fan comes on and after varying amounts of time then turns off like the powerlead has been cut. The amount of time it will turn on for varies from about 3 seconds to about 25 seconds so sometimes gets as far as wanting to start boot up and other times turning off at the HP logo.
For about the past 3 months the screen has not started straight away when I turned it on and I presumed it now needed to warm up, however restarting it would also do the same thing and thus the screen is actually fine. Now however the screen is turning on straight away when I press the desktop power button so I am thinking this is linked.
Considering that the computer is 7 years old, I would ask if there have been any changes to components or regular maintenance in that time. Parts can and indeed do get 'worn', and this can lead to a number of hints that something is about to give.
The 'fault' would appear to as others have suggested, or even a PSU problem, if that unit is 7 years old.
When you dusted out the computer, did you check to see if everything was seating correctly?.