You will also need to run Unregister on your old computer..
As far as I know you only need to un-register if you sell or otherwise dispose of the game. The registration of the game is not tied to a particular machine.
He will however need to un-install the game from his old machine as the license is only good for one copy.
Captain cadet: you could try simply swapping the hard drives and booting your new computer from your old hard drive. As long as it is windows 7 it should find all the drivers it needs itself. I have successfully done this in the past a couple of times.