Custom Landing Page Template: Display Categories as Images

Hi,

I’m developing my theme with a custom landing page. It’s going well except for one part:

In a nutshell, I want to call a specific category within a div and have it link to the given category page.

In detail:

See screenshot: http://move-onward.com/wp-content/uploads/2011/03/landing-cats.png

:: I have 12 different categories.
:: I want to display a specific thumbnail image for each category of the 12 categories, respectively. The image can be hardcoded and static.
:: When the use clicks the image, he/she opens up a page for that category, which contains all the posts in that category.

I’ve tried several methods, such as:

<?php
$cat = 7
$args = array(
  'orderby' => 'date',
  'order' => 'DESC',
  'post_type' => 'post',
  'numberposts' => 1,
  'category__in' => array($cat)
  );
$posts=get_posts($args);
if ($posts) {
  foreach($posts as $post) {
    setup_postdata($post);
    ?>
    <p><?php the_time('m.d.y') ?> <a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></p>
    <?php }
  }
}
?>

but nothing seems to work. I either get a blank page or nothing prints to page in the category block I created.

Finally, my PHP ability sucks. lol.

Any suggestions?

Thank you very much,

DC