IPhone music backup to new PC?

Hi, I lost my notebook in an accident last year. Now, I have a new one but am wary of syncing my iPhone to it for fear of it deleting my music on the iPhone. All my music was burnt on to the iPhone from CD's, I rarely buy anything from iTunes store. How can I get my iPhone music files to the new computer? Please, please no paid software referrals - I have seen those ads and don't trust them. I am sure Apple has a solution for this situation...just wanted to check with you guys as to the best FREE option that you have used to solve this problem. Thanks!