How to password protect a page template?

I am trying to password protect the template output on a page, but it’s not working. The template output just shows up under the prompt to ask for the password.

I’ve found this code but it doesn’t work:

if(!empty($post->post_password) and $_COOKIE['wp-postpass_' . COOKIEHASH] != $post->post_password)){
 // here what to tell the visitor: it's a protected page blah
}
the_content(); // here we ask WP to ask for a password, content should be blank

if (isset($_COOKIE['wp-postpass_' . COOKIEHASH])
 and $_COOKIE['wp-postpass_' . COOKIEHASH] == $post->post_password){
  // here it's the protected stuff...
}

When I put the stuff I’m trying to protect in the section there, it never shows up, even after entering the password.

I’m using a custom template within one of the themes from Elegant Themes.