Thanks for the link.
I was able to load the theme and get visual composer(4.2.3) running with Events Calendar Pro 3.7.
Unfortunately, I got zero errors in the process, not even a hint of trouble from my error logs, console, or query checker.
Although it appears to be an issue with The Events Calendar Pro and Visual Composer. To me it is starting to look like another plugin, some custom coding, or the hosting causing an issue.
Can you please copy the System Information from Events->Help into a reply and I can try adding some of the other plugins and see if that finds an issue.
Also, please contact your host and see if they they might have some insight into this. You could even share the url with this thread for them to have something to look at.
Let me know what you find out.
Thanks