i have a question about transfering music froma phone to a computer

My old computer crashed and I am trying to send my music from phone 5s to my new computer. I have deactivated the old computer from iTunes but when I connect the iPhone and try to change the settings to manually manage music it says it is still synced with the old iTunes. While I do have some music that I have bought from iTunes most of my music is from cds I longer have. When it wants to re synce then I will lose all my music I have not bought from iTunes. Any help on this?