I had the big brother to the 3100/E310, I had a 5100/E510. Two long and two short is not listed.  Lights 3 and 4 are memory related. Given the age, if the CMOS battery hasn't been replaced in the last 5 years start with that. CR2032 coin cell battery located on motherboard. Power off PC before replacing. Also, with it powered off, reseat the memory - unplug each memory module then reinstall. Here is the link to the Dell service manual, that includes blink and beep codes. Dimension 3100/E310 Service Manual (dell.com)  
Hi So I have broken the thing, I will get serial number etc as needed.   I cannot tell what I have inflicted on an old DELL desktop, and it now gives 2 long, 2 short beeps TWICE.   No screen output at all, and I suspect I have caused a CPU failure.   The front panel has a 1,2,3, and 4 illumnated number sequence, and 3 and 4 remain lit.     TIA.   What could I do next.    
Beeps 2 long 2 short twice.