The iPhone is designed to only sync with one computer.
Syncing with a new/different computer will wipe what is currently on the device and replace the contents with the media and apps from the new computer, there is no way around this. This is what iTunes and iOS are designed to do.
You did move your iTunes library from your old computer to your new computer, correct?
If not, here are instructions on how to do so: http://support.apple.com/kb/HT4527