Thank you for the detailed information. The fact that if the Revolution Slider is activated the Cornerstone is not responsive gave me an idea. It seems that you have not enough PHP memory limit on your hosting service and the server runs out of space when it wants to work both with Cornerstone and the Revolution Slider.
The other point I see is that I constantly see 504 error and sometimes the 503 error when trying to access your website. This is 100% a problem of a hosting service provider and most probably is due to lack of enough resources. You either need to consider changing your hosting service provider or using a none shared plan of your hosting.
You can check our hosting places if you are interested:
I installed the WP Server Info plugin and if you go to Dashboard > Wp Server Info you will see that the PHP memory limit is 256. Please increase that to 512, you may need to contact your hosting service provider to do so.
Kindly get back to us with the result of the test above, Another point that I suggest that you can test is to move your website to your local machine or a temporary other test server and check the result, that way you will see if the issue is from the hosting plan or not.