...the processor and/or motherboard could be toast. Unfortunately, there's not an easy way to find the problem without troubleshooting all the possibilities. A good cleaning involves taking of the cover and blowing out the fans, processor, heatsink, all tower openings, the power supply and everything else inside. So, try opening up the tower, use compressed air to clean out all the dust and while inside, check for bulging or leaking capacitors on the motherboard. If you find them, then motherboard may need to be replaced. In addition, make sure that all cables are securely connected to the motherboard and all hardware, including the power supply.
Next, by your description, the power supply could easily be the culprit.. Check with Dell and see if you can replace it with a similar PS but with more wattage..
HOpe this helps.
My Dell XPS 400/9150 with 1707 monitor is just over one year old. I also added a 22" Gateway monitor a few months ago. The Gateway monitor has had problems turning on which I assumed was a driver issue (no -hadnt gotten around to updating it) but just today the computer will not boot up. Sometimes the front fan runs for few second and then it all dies. I cleaned the vents in the front which were all clogged - the vents in back were clear.
--If it overheated, shouldn't it restart or did over-heating cause other problems?
--If the power supply is the problem, What kind should i replace it with?