Hey John,
Sorry to hear this!
I took a look and noticed something in the AJAX response in the console while viewing your site, so while this might sound weird and unrelated, I’m curious:
Your site’s events slug is /events—do you also have a Page in your wp-admin that is titled “Events”, and so it, too, is trying to existing at the /events URL on your site?
Head into your wp-admin and look for any pages that might be titled Events and/or otherwise are trying to use the slug /events. If you find such a page, delete it or change its slug to something other than /events. You cannot have a page and The Events Calendar itself trying to use the same /events slug. This will cause issues and seems to be an issue here with your specific problems.
Let me know if this helps!
George