Is this a wordpress-based site? If so, you will need to look into "domain mapping". It is a key concept that is often overlooked when trying to use folders as installations on a cPanel.
If you site is html/php, you will need to make sure that all of your access at the root level is defined in the .htaccess file. By assigning a domain to a folder you have to also manage .htaccess within that folder. I'm not an expert in the exact details, but I do know there are some good threads and @JHasselbring wrote an outstanding article in the GoDaddy Garage that addresses using multiple domains on a single cPanel server. Read this as a starting point!!!