I don't know the answer to the main question, but after a normal uninstallation method, you should reboot into Windows Safe Mode an run
http://www.avast.com/uninstall-utility.
Run aswclear several times under Windows Safe Mode, each time for each version of avast you ever installed or ever updated to.
Then search for any remnant (hidden) folder that may had been left behind, like "*alwil*" and "*avast*" (case insensitive). Delete them (still, under Windows Safe Mode).
Then reboot into Windows Normal Mode and install the latest stable version of avast. Once the installation finishes, reboot. If avast works correctly, test it a couple of days. Still works correctly? Renew the registration.
BTW, are you sure the specific "program" installation was already registered, or the "email address" was?
[EDIT]
Check the maintenance -> registration info. When is the expiration date?
[/EDIT]