Hi there,
It seems that there is a problem with the Plugin or the modal. I went to the modal settings and copied the shortcode which you can use as an inline element: [cp_modal display="inline" id="cp_id_9c5e1"][/cp_modal]
Then I added that in the Widgets area and it did not work, then I added a test page and added the code without Cornerstone and it is still not working.
I wanted to do another test but I can not as it seems your site is live. Would you please disable all the plugins including Cornerstone and only keep the ConvertPlus active and then change the theme from X to the default WordPress theme and check the test page to see if you can add the modal there or not?
If not then it should be the problem of the plugin itself. In that case, I will suggest that you downgrade the plugin version for testing.
Thank you.