Although iTunes won't copy non-purchased media from your iPhone into a new computer it can be done with various 3rd party tools... Cost generally ranges from reasonable down to free. The "manual" method of extracting the files in disk mode that could be used with older iPods won't work without the addition of a tool to gain access to the iPhone's filing system such as
iPhone Explorer (free).
All in all maintaining a proper backup of your iTunes library is a lot less hassle, but never say die. If the data still exists there's usually a way of getting at it.
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