How to sync music from old PC to new PC? I have a new iPhone 6 and need to get my non-purchased music from the old iPhone 4S to the new phone.

When I connect to iTunes on the new PC (with the old phone) and select Sync Music I get the warning asking me if I'm sure, and do I want to remove existing music etc. from this iPhone. And of course I don't because all the music I need is on that old iPhone. The old PC crashed and is no longer available. How can I transfer the songs to the new phone without having access to the old PC that the 4S used to sync with?
I backup all media contents from my old iPhone 4 to iCloud, and then login the same account on the new iPhone 6, and then sync all media to the new phone, quite convenient.