Thank you for the reply. First, I appreciate your word of caution but as an ex-grad student of physics (and having worked with electronic/capacitor-containing devices for 40 years, including PCs for two decades), I know how easy it is to get seriously injured or worse). Thank you, though, it never hurts to be sure.
I am sure it's the fan. I have the side cover off and can insert a small straw through the metal mesh and slow it down or stop it briefly. The sound disappears. I can hear it clearly when it starts to vibrate and whine again. I transported it recently to a friend's house and my guess is that the journey changed the central rotor or affected the bearings or something else just enough to cause it to whine.
It's good to know that the fan is replaceable. However, I live in a rural area in Idaho and getting a replacement would be best over the Internet, if possible. Do you know of any likely sites for that?
Thanks again for your prompt, clear, and well-worded response.