sync iphone with new computer without removing items from iphone

If you do not have access to the iTunes Library on your Old computer... or its Backup...

See these 2 Links...

Syncing to a New Computer...

https://discussions.apple.com/docs/DOC-3141

Recovering your iTunes library from your iPod or iOS device

https://discussions.apple.com/docs/DOC-3991

If you do have access... See Here...

iTunes: How to move your music to a new computer

Or...

From your OLD computer...

Copy your ENTIRE iTunes FOLDER to an External Drive... and then from the External Drive to your New Computer..

Full Details Here > http://support.apple.com/kb/HT1751

Unfortunately, the only thing you might be able to try, from my knowledge, is to go to the other computer (the old one you synced it with) and copy over the entire iTunes library and files to the new one, and try that... but even still, I believe it's a no go still. 😟