Wow! I started this thread as more of a heads up than a request for help -- I sure didn't expect all the responses I got. I did another search of both this forum and the web generally and found several others with the same symptoms -- and no help for any of them. For me, as I stated originally, the problem is gone since I doubled the memory to 512mb.
Since this is my wife's laptop, there is very little that starts up during boot. Avast does, of course, and Windows Defender, plus stuff that installed with her HP All-in-one printer. I have gone through the things that start up and eliminated any I think should not be there.
I have set the setting in Windows Defender which keeps it from scanning at boot time.
I have defragged her disk (and she does it too) sregularly.
I set avast not to start until after system programs have started.
Discussions about adding more memory beyond the 512mb we have now is pointless -- this is the maximum the system can support -- and besides, it used to be fine with just 256mb.
Avast replaces McAfee for antivirus. My wife runs adaware regularly, and I run Malwarebytes, asquared and ccleaner, too.
I have also booted with the wireless network card removed, so the internet was not available.
None of these had any measurable effect on boot time.
Note that unlike many people's problems, there is little cpu activity, with more than 90% available. However, I can hear the hard disk chugging away throughout the boot.
But again, remember, I don't really have this problem anymore...