1. Disable automatic syncing on connection: iTunes Prefs > Devices > Disable
2. Connect Phone
3. Right-click device tab (left iTunes window border) and select "Transfer Purchases." )Or, File > Transfer Purchases from iPod.)
4. Right-click device again and select "Backup."
Make sure the new computer is authorized and signed into your iTunes account.
I have this problem but since the library doesn't recognize my iphone anymore and thinks it is associated with a different library, it won't let me back up the music files without deleting everything on the iphone first
All this happened after a software update and I hadn't noticed it until I have a big discrepancy in the files in my iphpone and those on my pc. I tried transfer purchases but not everything was purchased from iTunes