Title don’t function as link

You need to put it inside the <h3> tags:

<h3 class="slide_title">
    <a href="https://wordpress.stackexchange.com/questions/82417/<?php the_permalink(); ?>" title="<?php the_title_attribute(); ?>">
        <?php
            $long_title = get_the_title();
            $short_title = substr( $long_title, 0, 55 );

            if ( strlen( $long_title ) !== strlen( $short_title ))  {
                echo $short_title . '&hellip;';
            } else {
                echo $short_title;
            }
        ?>
    </a>
</h3><!-- .slide_title -->

I’ve also fixed up your title code for you a bit 🙂