How to move my iphone and its contents to a new computer?

Our computer that we use to sync our iphones (same itunes account) has crashed. All of the files are saved to carbonite.com, which is great, but I'm having trouble figuring out how to get the things that are on our iphones (that were not backed up the the old computer, and some that were) to sync with the itunes program on our other computer. I have plugged the phones into the new computer, and get the message about deleting the iphone's contents and syncing it with the new computer. We have our settings set so that our phone data is on icloud, but I have no idea how to get it back onto the phones after resetting them I don't want to do something I can't undo! Can anyone offer up some advice? If I "delete" the contents of our phones in order to sync them to a new computer, how do I recover our apps/music from the cloud, or will it just be there when I get through the process?

You can use a 3rd party software like this iPhone file transfer, it can work as an iTunes alternative to transfer songs, videos, photos, contacts, apps, etc from iPhone to computer, hope it helps you.

Please check this great iTunes alternative which called TunesGo, it would help you easily transfer the files on your iPhone to the new computer and manage it.

You can try some iOS transfer tool that helps you transfer contents between iPhone and computer without erasing any precious data. AnyTrans ( http://www.imobie.com/.../anytrans/ )does great in transferring iOS data. You should try it!

IPhone Transfer Platinum allows you to transfer various files like music/movie/Pictures/TV Shows/Podcast/iTunes U/eBooks/Camera Roll/Ringtone/SMS/Contacts/Voice memos/Camera shot files from iPhone to your new computer.