I have a new computer and I want to "sync" my iPhone with it. All information is on my device (iPhone) so I don't want to replace what is on my device with nothing (as this is a new computer). How do I do this?
The iphone is not a backup/storage device. It simply mirrors the selected content of the computer to which it is synced.
Copy everything from your old computer, or your backup copy of your old computer to your new one.
I don't have access to the old computer. It died.
See Recover your iTunes library from your iPod or iOS device.
Also see this user tip...
Syncing to a "New" Computer or replacing a "crashed" Hard Drive
Retrieving data ...