Repair avast!:
1. Control Panel -> Add/Remove programs -> avast!
2. Click on 'Repair'.
3. Follow instructions.
4. Reboot.
Did all that, but the registration request popped up after a few days. So I registered with a different name and email which were accepted, so I'm set until the other registration expires.
Not a major problem, but judging from this and other problems reported here, it's yet an other example of the increasing sloppiness of Avast's programming.