How do I transfer my itunes playlist on my ipod to itunes on my new computer when my previous computer crashed and cannot be accessed using the "home sharing" option?

I have an existing ipod classic which contains a playlist that is a mixture of my own uploaded CD's, as well as purchased songs from the itunes store. I have a new computer that replaced a previous computer that crashed and which contained the ipod playlist. I've been able to to restore my purchased songs from the itunes store on my playlist on the new computer, but don't know how to get my ipod with its existing playlist to sync in to my new computer's itunes playlist - the new computer's playlist only contains purchased tunes from the itunes store - the playlist on the new computer needs to be updateed with all the songs on my ipod - not just the purchased itunes store songs.