I sorry for the issues.
It sounds like the system thinks the plugins for the Events Calendar are not the same Version.
When you go to the Plugins Page of your site.
What is the version number for:
The Events Calendar
and
The Events Calendar PRO
Those two plugins should have the same version number.
Downloads
If you need to download the latest version of pro you can do that on tri.be in Account Central section after you sign in.
The latest version for The Events Calendar can be found on WordPress.org.
Let me know what you find out and we can go from there.