Searching through other posts, I round reference to the /Cleanreminders command-line switch. I tried it, first by temporarily editing my shortcut, and then directly in the command line "Run" window... "C:\Program Files\Microsoft Office\Office10\Outlook.exe." /Cleanreminders. I have returned my shortcut to its original state, which uses the /Recycle switch.
Now when Outlook starts, I get a balloon over Outlook's icon in the system tray that reads as follows. "Cannot start the reminder service. Unable to show reminders."
