Is this right? You have a domain with Drupal as a subdirectory (http://www.example.com/drupal, perhaps at /var/www/vhosts/example_com/drupal) and also want another domain to serve only that subfolder (http://drupal.greatdomain.com), but http://drupal.greatdomain.com is serving the same content as http://www.example.com.
Are you restarting Apache after changing my.conf? Could you post that file (anonymize what you like), or at least DocumentRoot?