Music sync is one way. Computer > Phone.
Copy the music for the computer you were using before to your new one and import them into iTunes.
The phone can only sync with 1 iTunes library at a time. Setting it up to sync the music from your new computer requires erasing the media from the phone first.
syncing to a new computer http://discussions.apple.com/docs/DOC-3141
Iphone is not a media storage, so you can't copy songs from your iphone to itunes, only itunes to your iphone.
did you copy your itunes medial library from you old computer and put it on your new computer.