If the "Registration→Registrations" menu item is disabled then IDM is already registered and you do not need to do it again.

'Registration→Registration' menu item is disabled

If you use "Help→About IDM" IDM main menu item you should see the word "Full" after version release date (arrow 1 on the image) and your name (arrow 2 on the image).

Check that Internet Download Manager is registered on 'About' dialog