Problem solved: I have downloaded my version of Avast! Mac Antivirus through Cnet some time ago. They offered the wrong edition, i.e., the Pro edition instead of the Free edition. The difference between these editions is explained here: http://www.avast.com/en-us/faq.php?article=AVKB72#idt_07

I have uninstalled the Pro edition, and installed a fresh copy of the Free edition instead.
In the subscription screen the “Register now” button is visible again.