There have been extensive discussion so this problem on the Dimension - General Hardware forum over the last few years.  In many cases, it was the result of a failing hard drive.  Once the hard drive was replaced the problem went away.  For others, the problem was not so simple.  The first thing to check is the diagnostic lights on the back of the computer.  When the message appears to hit the Delete key, look at the diagnostic lights.  They give a code that might lead to a solution to the problem.  Interpretation of the code can be found in the following document:

http://support.dell.com/support/edocs/systems/dzuul/codemess.htm

Steve