When I right click on a particular printer and try to view the
Properties of it, I get the following message:

Printer properties cannot be displayed. The print spooler service is
not running

Problem is, it is running, as going to Administrative Tools -
Services in the Control Panel verifies.

One of the "printers" I have installed is "Send To OneNote 2007". I
can right click on that just fine - just not this other printer.
Would I be able to do that if the print spooler wasn't running?

Indeed, if I do disable the print spooler, *all* the printers in
"Printers and Faxes" disappear. So the fact that I'm even seeing them
in the first place suggests to me that the printer spooler is running.