The last time I had this problem with a Dimension 8000 it turned out to be the PSU. I couldn't find any information on the web about what the beeps meant. I got it down to the PSU because I tried a new hard drive and tried swapping the memory.
You could try reseating everything (audio, video, etc.). If you have a warranty I would contact Dell (via phone or web chat) and run the beeps by them.