O Death, where is thy Sting? (or Bono)

You haven't mentioned what happpens when you connnect to your computer.

Trying to do something with a dead device on its own never yields much info. Your PC is your diagnostic device for looking into the heart of that thing. Does your PC "Ping" when you plug in the USB cable. You may have to wait for several minutes.Your USB could be struggling to charge up a dead or shorted battery. If anything at all appears in the bottom RH corner of your computer screen then you have a ray of hope.

Try this - if you haven't done so already.

Personally, i'd take the whole thing to bits and put it together again and plug it in (works for cars[maybe without the plug it in bit but you get my point]) Add a new battery first (again works for cars and iPods often) then your iPod should tell you what its problem is by its error code, or maybe its just old and fed up with its software and wants the funky new (3.1 lol) software update, works for me a lot of the time.