The pages you are trying to edit, is this previously built in Cornerstone? If not, you have to build it from scratch using Cornerstone. Cornerstone builder like any other builder cannot pickup how other page builder built the elements. There's no one button function that will transfer content from different builder.
Also, the backup you have restored, is this from a different install? Or is this a database backup of same installation? I have visited your site and it is under maintenance. We might need to check your site setup. Please share credentials inside a secure note