Comment_Reply_Link Not Showing?

My suggestion would be twofold:

1. Ensure you are properly enqueueing the comment-reply script
2. Replace your hard-coded comment list with wp_list_comments()

Enqueueing comment-reply

I would recommend hooking into comment_form_before():

function wpse71451_enqueue_comment_reply() {
    if ( get_option( 'thread_comments' ) ) { 
        wp_enqueue_script( 'comment-reply' ); 
    }
}
// Hook into comment_form_before
add_action( 'comment_form_before', 'wpse71451_enqueue_comment_reply' );

Outputting the comment list

Using wp_list_comments() with default output in your code:

<?php if($comments) : ?>  
    <ol class="commentlist">
        <?php wp_list_comments(); ?>
    </ol>
<?php else : ?>  
    <p>No comments yet</p>  
<?php endif; ?>  

If you need specific markup for the comment list, you can pass a callback as a parameter to wp_list_comments(). But I would strongly recommend making sure everything works with the default output first, and then try to customize.

You can use your own custom markup in a callback, but you’ll need to be sure to define the variables you’re using, such as $depth and $args. If you can provide specific markup questions, I can help construct the callback.