You will need to install the software on the new computer just like you did on the previous computer.
You will need to re-register those BSB4 charts (you'll need a new Activation Code.)
Also, Offshore Navigator can be updated to the latest, v5.08 by clicking here
If you have any routes, marks, tracks, or named waypoints you want to move over, in the File menu in Offshore, on your old computer, you'll find an option to Export Data to File.
Move the exports to the new computer and then use the Import Data from File option.