[Plugin: Sideblog WordPress Plugin] randomize sideblog posts

Not sure what your sideblog is doing, but this will display a random post from category 1:

<?php
//list a random post title from one category
$cat = 1; //category ID
   $args=array(
   'category__in' => array($cat),
   'orderby' => 'rand',
   'showposts' => 1,
   'caller_get_posts' => 1
   );
$my_query = new WP_Query($args);
if( $my_query->have_posts() ) {
while ($my_query->have_posts()) : $my_query->the_post(); ?>
<p><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></p>
<?php
endwhile;
}
wp_reset_query();  // Restore global post data stomped by the_post().
?>