Here is what finally worked for me. Based on some hints that I found on www.codecguide.com, I downloaded Codec Tweak Tool 6.1.8 from www.videohelp.com. I installed and ran it, then clicked the DirectShow Filters button under Configuration. On the Filter Configuration screen, I clicked the ffdshow video decoder (x86) button, and found that the H.264/AVC format’s decoder was “disabled.” I selected the “libavcodec” instead, then clicked Apply and OK. After exiting from the Codec Tweak Tool, I restarted the computer and loaded one of my freezing presentations into Impress. Success! The slides containing avi videos now display with no problem in Normal View, Slide Pane, Slide Sorter, and Presentation.
I have no idea how the original problem happened, but I’m very happy to have it working again.
(Note: one tidbit of information that helped confirm I was on the right track is that LibreOffice uses DirectShow to display videos on Windows. So that was the piece that was failing for me, and that’s where I could concentrate my efforts.)