How do I move ALL songs from iPhone to A new iTunes?

So, I have a pc, iPhone 3GS and a IPad 3rd generation. I got the phone a long time ago and sadly the computer I originally synced it on is broken and so I have to use my new pc, is there any way that I could sync my phone on the new pc without loosing all my music? I understand that the music I have bought via iTunes will

Be safe due to the iCloud but what about the music I got through CDs? If I don't own the CDs anymore will I just loose the music? If so I think this is a giant inconvenience that apple should certainly seek to improve their service for consumers in my circumstances.

Thanks for the help! :)