Hard to say... some Dell models use standard sizes and connectors and some don't. Some use standard connectors but wired in different ways... without knowing specifics about the models and such, you could actually cause a fire by trying to make it work.
Saying it just makes beep sounds doesn't help too much. Could be a bad processor, motherboard, RAM, BIOS chip, video card...
Could you get us the following:
- Specific Model # of your Dimension (usually 4 digits on the front of the case)
- A more specific pattern of beeps
- Do you hear the fans turn on? (You may need to open the case and look to see if they are spinning, should be at least one fan in the back, one inside the Power Supply, one on top of the processor.