Thanks for the suggestions.
In fact, out of desperation earlier today I reinstalled avast! Free over my existing install without uninstalling it. (The latter had started displaying the dreaded red popup: “avast! Information. Your subscription for avast! Pro Antivirus has expired. As a result, the program will not download any further updates.”
I’m now back to the regular white avast! Free Antivirus interface, for whatever that’s worth. And I then updated the program to version 8.0.1488. If these steps don’t solve the problem, I’ll go through the whole routine again using the tools you mention.
Maybe worth knowing: I have avast! Free installed on another machine, also running XP Pro SP3, on which the screen saver wouldn’t activate. Updating to 8.0.1488 seems to have solved that problem.