Sounds like your CPU is overheating or has become detached from the heat sink.
Pretty common in the older dell computers, you can get some thermal paste from radio shack, remove the fan shroud and unscrew the heat sink screws on the motherboard, remove the heat sink, clean the bottom of it with rubbing alcohol and if need use a razor blade to scrape off all the old thermal paste.
Clean the paste off the CPU as well, but don't scrape with a blade, to remove the CPU look for a bar that lifts or a screw that turns 1/4 turn, either of these will unlock and release the CPU.
Be sure when you do it that you are grounded, that means not on a carpet, shoes on, feet on floor, then hold the chassis of the computer so that you are touching the same ground point the CPU does. You can leave the computer plugged it, but be careful not to power it up during the process.
After you have removed and cleaned the heat sink, replace the CPU, put a dab of thermal paste on it, do not over do it or goop it up, then reseat the heat sink.
Here is a YouTube on the basics of how to do it.
http://m.youtube.com/watch?feature=r...&v=trNQynvFjSU
They use some various cleaning chemicals, but I have found rubbing alcohol works just fine, don't use any type of linty towels, coffee filters work great and don't pour anything on the parts but rather put the alcohol on the towel/filter and use some elbow grease to scrub it off.