Don't you have the Activate button shown in the link i posted? Is'nt the product on your Arturia account?
You can allways uninstall the Demo, and instal a new application. But the application is the same.
But check your account to see, if it's there. It should be there, if you have bought it through Arturias website. It should actually show up in ASC.
I have never used a new serial number to activate a demo. But i can't tell if that's needed now. I can't recall if i have had a trial to be exspired. I think perhaps i recall some had to download and install the new application long ago.