Okay, I don't know how, but it seems to be good now.
I shut down my computer last night, and when I turned it back on this afternoon, the "virus definitions are out of date" warning was gone. It now said the application needed to be updated though. First, I tried running a repair, just to be on the safe side, and that finally worked. Then I updated the app, restarted, and it seems to be fine.
Thanks for the help.
Hi David,
We appreciate your efforts in providing us all the possible information regarding your query.
Unfortunately, we're unable to view the screenshots through the provided links (except our Community link).
To share the screenshots here, you can click on Answer - Select mountain symbol - Browse & attach them.
However, from your description, we see that either the program is unable to communicate with our server or the downloaded patches are not applied to the program.
Also, we see that a setup is already running in the background which blocks the repair process.
In this regard, we'd suggest you to restart your computer once & check if the patches are applied.
Hi David,
We appreciate your efforts in providing us all the possible information regarding your query.
Unfortunately, we're unable to view the screenshots through the provided links (except our Community link).
To share the screenshots here, you can click on Answer - Select mountain symbol - Browse & attach them.
However, from your description, we see that either the program is unable to communicate with our server or the downloaded patches are not applied to the program.
Also, we see that a setup is already running in the background which blocks the repair process.
In this regard, we'd suggest you to restart your computer once & check if the patches are applied.
I'll try my screenshots again:

Glad to hear that, David.
We appreciate your efforts and time.
Feel free to contact us if you need assistance with AVG.
Have a nice day!