Most of yesterday was spent downloading software, updating virus definitions and scanning the three large drives on my computer. I think I've finally found all my problems and that I'm now running Trojan and spyware free. *whew*
I started out by scanning my drives for junk, old temp files, that sort of thing. I pulled over a few gigabytes of garbage and dumped it all. (using Wise Disc Cleaner, the free version). I plan to run it again today and see what else is lurking about. Yesterday I only hit major directories.
Then, I ran Malwarebytes' AntiMalware program. It found a bunch of stuff. Nine infected or suspicious files, an infected folder and four registry entries/keys/etc that required cleaning or quarantining.
Finally, I ran full AVG scans of everything. It found and cleaned up a couple more items.
This morning after a restart, my computer is running somewhat faster than it was before, and I'm certainly not getting any irritating antivirus popups, "infected file blah-blah-blah requires action." I've uninstalled F-Prot, my previous virus protection, as it didn't find any of this stuff. It popped up occasionally with a warning about something, but repeated scans didn't actually find (or more importantly, eliminate) the trouble.
We'll see how this goes. The software I'm now using comes highly recommended by CNET editors and users, so I'm quite hopeful.