Rebooting is now much faster, although still slow. (There are a lot of things loaded onto this computer.) And when it finally comes to an idle, the computer stops ticking the hard drive every five seconds. So I think I can safely conclude that it's the Symantec software causing the problem.
Meanwhile, the disk tools told me that the hard drive is something like 40% fragmented, and that's not good either, so I'm running the disk defragmenter, which of course will take many hours. I will then see if it's possible to just install the anti-virus software, not all of the other bits and pieces of the Norton suite, and if so, will that make a difference. Of course I'm out the $70 spent on software that makes my computer run worse, but I don't think there is much I can do about that.
Mind you, what I should be doing is cleaning the house, putting all of the stuff that's sitting on the floor into boxes and the boxes into the storage closet. The carpet cleaners will be here on Monday morning, and I need as much floor space free as possible so they can clean the maximum amount of carpet.