<?php
$posts_count = 5; // The number of posts
$days_range = 7; // To fetch posts published during the last 7 days
$title_length = 40;
$result = $wpdb->get_results("SELECT comment_count,ID,post_title, post_date FROM $wpdb->posts WHERE post_date BETWEEN ".(date("Y-m-d H:i:s",strtotime(date('Y-m-j H:i:s')) - ($days_range * 24 * 60 * 60)))." AND ".date("Y-m-d H:i:s")." ORDER BY comment_count DESC LIMIT 0 , ".$posts_count);
var_dump($result);
foreach ($result as $topten) {
    $postid = $topten->ID;
    $title = $topten->post_title;
    if(strlen($title) > $title_length){
        $title = substr($title, 0, $title_length) . '...';
    }
    $commentcount = $topten->comment_count;
    if ($commentcount != 0) {
    ?>
    <li class="clearfix"><a href="<?php echo get_permalink($postid); ?>" title="<?php echo $title ?>"><?php echo $title ?></a></li>
    <?php }
}
?>