If your Dell has a Windows XP operating system, you should think about buying a new computer.
In April windows XP will no longer be supported so its almost time to replace the system anyways.
The cost of diagnostics and repair of your current system will be close to the cost of replacement.
For $300 you can get a much more powerful system than you currently own that comes with a warranty.
If replacement isn't an option then there are a few easy things we can try to see if we can diagnose it for you.
I am going to assume your using a desktop, if you have a laptop your probably SOL
1.) Unplug the system and remove the cover. Remove as much dust as you can either with compressed air or by manually blowing the dust out. Do not use a vacuum!!! Make sure to get inside the power supply and any/all fan and heatsinks. Replace the cover, reconnect the cables and power the system on. See if results are better.
2.) Unplug the power and remove the cover. Place on a flat surface where you have a good view of the insides. Locate all the fans within the system. Reconnect power and turn the system on, visually inspecting each fan for rotation. If any of them fail to spin they will need replaced.
Without the included resource CD and operating system disk this is as far as you should take the repair process. If you have a friend that has the disks you may be in luck but if not then the economy of fixing the system is no longer viable. Purchasing a replacement disk is anywhere from $100 to $300 if you can find them. At this point if the system is not functioning its time to save for a new one.
Good luck!