Just in case this might help someone.... I have been struggling with cornerstone 6.1.3 not loading for a couple of days and I was able to correct it on a staging site and a production site by upgrading to the latest version of WordPress and re-validating X from the cornerstone home section. (You also might want to check your php version). Although my version of X 6.1.3 says it is validated, my cornerstone home section is still telling me I have to validate cornerstone... but it works. I tried everything else I could find on the forum but none of it worked for me.
Hope this helps : )