transfer non itunes purchased music from Ipod to Itunes

I have an ipod nano 3rd generation with music content (CDs and Itune purchases) that was synced to an iTunes library on an old pc that crashed and was never recoverable.

I now have another pc with a new iTunes library and content different from that on the IPOD.

I would like to transfer the content of that old ipod to the library (in a nut shell I do not wish to take out all my cds and install them manually on the new PC to have their content available for iTunes.

I pod pages say you can only transfer music from an ipod to iTunes if that music was purchased from iTunes and not if it was from CDs.

Is there a way around this or do I really have to transfer my CDs one by one to the new Itunes

Not: I am willing to buy iTunes match if that helps...