I am sure that the driver installation will need to have registry entries, which are normally made by the installation routine.
I lose the will to live when faced with HKEY_Classes_Root, so good luck in trying to identify them on the working system and then copying them across!
The HP driver page for the 4070 has a >300MB file for the "4070 series" - is this the file you have downloaded and found wanting?
HP Image Zone Software HP Scanjet 4070 Photosmart Scanner - HP Customer Care (United States - English)
I note it states that:
However, this download does not contain any third party software.
Is it possible that the slide scanning features are provided by an additional software package, that you might still have installation media for?
SD