You can only sync an iPhone to one computer. You cannot connect it to a computer different from the one it syncs to and drag music onto it.
If you want to be able to drag music onto your iPhone from the computer that it has been syncing to you must check the "Manually manage music and videos" box under Options on the iPhone page in iTunes. This will change your method of syncing from automatic sync to manual sync, and will erase all music currently on your phone to set up this new method of transferring music to the phone.
The better way to do this is to NOT use "Manually manage..." and instead create a playlist in iTunes of all of the music you want on the iPhone. Drag all of the tracks you want on the phone to this playlist, then click the Sync button.