Getting music off of an iPod classic

Hi Everyone,
Heres the situation:

I have an Ipod classic (5th Gen I think, white, 60gb) that I used for almost three years no issue. I have tons of music on it. My dock cable developed a short and it took me a while to figure that one out. Obviously something got messed up because it wouldn't (and still won't) connect to my computer ( I get the USB not recognized message when I connect it). It will play all the songs.
I can get it charge on my car charger through much manipulation. After a few months of headache I bought a new iPod classic. I didn't back up my old library (stupid I know) and now I only have a fraction of the tunes I like on my new iPod.

Question.
Is there anyway to get the songs off of my old iPod onto my computer? I googled it and read through most of the software descriptions, but it seems at one stage or another the computer has to recognize the iPod in some fashion and mine won't
Thanks for your help