Update to the latest version (18.1.2326) and try again: https://forum.avast.com/index.php?topic=215365.0
And now 20 minutes, two reboots, a butt load of firewall alerts and and about 5 minutes of hard drive activity later, it appears to be registered. I now have a whole year before I have to go through all this again.
Why two reboots? Avast needed one, then I had to reboot into safe mode, so I could get rid of the misnamed "Emergency Updater". Misnamed because the stupid thing runs ALL the time. My firewall alerts me when new programs try to access the net, and the very first time Avast ever included this, it kept popping up alerts about this pain in the ass program, always with a different random filename, so I couldn't even permanently authorize it, even if I wanted to. I deleted it and I've deleted it after every update.
And if you tell me that this is the reason that registration wasn't working, please be prepared to explain how registration qualifies as an emergency.
Plus, as I was typing this message, there was a flurry of hard drive activity which Process Monitor says was caused by Avastsvc.exe scanning pretty much the entire drive. I didn't tell it to do a scan, so why is it accessing all the files and directories? I see the main window telling about all the supposed problems with my system and wanting me to click the Resolve button. Was Avastsvc.exe really grinding my hard drive for several minutes just for the purpose of trying to selling me something? I'm afraid to click the Resolve button to find out, because if it's not an ad, I don't want it to go and delete something that I might want to keep.
I use Avast as an anti-virus program. I don't want it trying to screw with other aspects of my system.
This is why I put off updating as long as possible.