Changing comment author link

I have a function that makes the comment author’s name link to a profile on my site. It works great … except for the fact that it displays either Mr WordPress when the admin comments or anonymous when other users comment. I’m not sure how to change this – my php skills are rather limited – hope someone can help. One I get rid of this function, the names show properly but it will link to the comment author’s website (if they have one listed) and not their profile. I just found this function after a google search and I’ve tried messing with it but it’s not doing anything i want it to do – bad php code ??

function new_comment_author_profile_link(){

    /* Get the comment author information */
    global $comment;
    $comment_ID = $comment->user_id;
    $author = get_comment_author( $comment_ID );
    $url    = get_comment_author_url( $comment_ID );

    /* Return the default WordPress comment author link if comment author is not
    a registered user */
    if ($comment_ID == 0){
        if ( empty( $url ) || 'https://' == $url )
            $return = $author;
        else
            $return = "<a href='$url' rel='' class='author-url'>$author</a>";
    } else {
    /* Return the link to the comment author's profile page if otherwise */
        $return = '<a href="'.home_url().'/?author='.$comment_ID.'">'.$author.'</a>';
    }

    return $return;
}
add_filter('get_comment_author_link', 'new_comment_author_profile_link');