By serendipity, I discovered the answer to my own question:
To those of you who are having problems with AOL's software not showing your buddy list, etc., when you log on, simply do this: delete your existing copy of AOL from your "Applications" folder and then reinstall the AOL software onto your desktop and leave it there. When you do this, everything in the AOL program works as it should. I'm not sure why this fix works, but it does. :-)