RE: The only other thing I can think of is that I briefly enabled WP Super Cache, but then decided I wasn't going to use the plugin, so I de-activated and removed it. Don't think this is a problem though because the plugin is no longer installed.
This has previously been reported as an issue with WP Super Cache in this forum. Apparently the WP Super Cache plugin is not fully removed when deactivated and creates an ongoing error.
Gilb2406 being able to fix his problem by reinstalling WordPress indicates this may have been the source of their error.
I believe that the changing URL factor is a further symptom of problems on the relevant site rather than a root cause.
The real cause is most likely a Javascript Conflict caused by the theme or another plugin.
Like many other popular plugins, CF7 is frequently reported as not working in the WordPress Forums when the real cause is conflict from another theme or plugin.