prueba esto en tu sentencia SQL
Lo único que te añadí es:
AND f.forum_id NOT IN ($no_mostrar) Código PHP:
$sql=mysql_query("SELECT t.topic_last_post_id, t.topic_title, t.topic_id, t.topic_time, t.topic_replies, u.username,u.user_id, f.forum_name, f.forum_id, p.post_id, p.post_time FROM ".POSTS_TABLE." p, ".TOPICS_TABLE." t, ".USERS_TABLE." u, ".FORUMS_TABLE." f WHERE t.topic_poster=u.user_id AND t.topic_id=".$value." AND p.post_id=t.topic_last_post_id AND t.forum_id=f.forum_id AND f.forum_id NOT IN ($no_mostrar) ");