Do you know if your Dell use an integrated graphics adapter or if it is a stand-alone graphics card? The GPU (the video card/adapter) may be defective.
How old is the system? Also, what operating system are you using (XP, Vista, Win7, etc)?
Last, what GPU does your system use (you can find info in your Display Properties)? It is likely either an Intel, ATI, or Nvidia device. It may be possible (hopefully) that all you need to do is update your drivers.
Dig up this info and we'll try that first, certainly won't make any worse and may solve the problem.