How sync to new computer without losing all of my music

My old computer finally crashed and I had all of my music on there. The songs are all lost. Most of it was from CDs I had (100s of CDs) that I no longer own due to a house fire a few months back. The only versions I have of them are on my iPhone 4S so I don't have any way to back them up because in order to sync to a new computer you lose everything and get whats on the new one conputer.

I have no idea how to save the ~1300 songs that I have from all those old mix CDs and stuff because I need to get my phone set up with this new computer and sync new music.

Is there anyway to guarentee I will not lose my entire library?