I spent some time that night trying to figure it out, and got nowhere. I rebooted, obviously; no help. I decided to defrag my hard drive, which went without a hitch. My regular AVG scan started Friday morning, and took 11 hours to complete (it normally takes 5 hours). The AVG scan report showed 26 suspected viruses, virtually all in copies of e-mail inboxes that I had made years ago when my computer was serving as a backup while I gave those computers a new hard drive. I don't have the report at the moment, but I think the viruses were some bagel virus, some Netsky virus, and I can't remember what the third one was. However, because I never accessed those e-mail inboxes, there would have been no reason for any virus to ever go active.
On Saturday, I came back to the office to try to figure things out. I found that my AVG was now essentially disabled -- the .exe files and most of the .dll's had disappeared from that directory. So now I have no anti-virus software. I tried doing a system restore to before I had a problem; it didn't help.
I honestly don't think that the viruses that AVG found are the problem -- they are in directories that have seen no action in years. (I can't remember having looked at the AVG log before -- we just got upgraded to 8.5, and I think some new settings on the upgrade version resulted in the results of the scan hitting me more in the face than before.) But I don't know what could be going on. I have done all of the things that the Preparation Guide talks about.