After some time investigating the issue, I found these following errors that might be causing it. But first please do not attempt to edit your page outside of Cornerstone or else you'll lose the ability to edit that page back in Cornerstone, when I check your homepage it was defaulting to visual mode (see screenshot -1 below).
The first issue is with regards to FontAwesome, not only with PRO but with the fontawesome on Strong Testimonial plugin (see screenshot -2 below). The most common cause of receiving a 404 for Font Awesome is on a Microsoft IIS web server, IIS doesn't enable the .woff or .woff2 mime type by default, so we'll need to add some additional rules to the web.config for this.
Open up your web.config file (this is for IIS 7 or later) and add the following:
<mimeMap fileExtension=".woff" mimeType="application/x-font-woff" />
<mimeMap fileExtension=".woff2" mimeType="application/x-font-woff" />
If you're not comfortable doing this, please contact your hosting support to assist you on this matter.
cs.js file are throwing an error (see screenshot-3), when I check this files, yours seems to have a lower size than it should be, so its either these files are cached/optimize or worst corrupted. I know that you don't have a caching plugin, but is there any chance that there is a server-side caching? Please contact your hosting to confirm this as well. Re-install the PRO theme to make sure that you have a clean copy of it and none of the files are corrupted.
Third, I notice that you have this Cornerstone La Hacienda Extension plugins, this seems to be a 3rd party Cornerstone add-ons, it could be the culprit of the issue, would you mind to deactivate this and clear any caching feature the site might have.
Let us know how it goes,