I had a similar issue when I upgraded from v4 artist to v4 pro. In the studio one activation window, there is a check box that asks if you are upgrading from a previous version, and then asks for the product key when checked. When I checked that box, it wouldn't allow my product key from the artist version, so I just left the box unchecked as if this was the first time I had installed studio one on my computer and it seemed to work.
Either way, if you purchased v4 pro and have a product key from presonus you should definitely be able to install it.