The first problem was when I received this error message when launching iTunes, and the Bonjour service wouldn't start. The second problem was that my MySQL database service failed silently, and my Query Browser didn't find any local database running.
I went to Control Panel --> Administrative Tools --> Services, and found those two services with no status. When I tried watching them manually, I got the same error.
Internet advice recommended that I reassociate *.msc files with mmc.exe, but that was already the case, and redoing it didn't help.
The Event Viewer showed Event ID 7000, and a Google search took me to this page, which advised me to try sc query MySQL. The exit code was 0, consistent with a file permission problem, so to locate the file that needed its permissions adjusted, I went back to the Services panel, right-clicked on the service to view the Properties, and found the executable path. Stripping off the “MySQL” at the end, I launched the command and received a Windows Firewall alert! I granted permission, and MySQL started perfectly.