How to list all categories and their posts under them - Implement in accordion

Hi all, I'm very new to PHP and I don't know much, I had this idea I wish to implement on my blog using the Wordpress platform and I am looking for some help.

What I'm trying to do here is create an accordion which lists all categories and their posts under them. For the accordion I used the simple accordion demonstrated here: http://www.dezinerfolio.com/2007/07/19/simple-javascript-accordions/.

Ok so first I needed a code to list all my categories with their respective posts under them as permanent links. With some research and personal mumbo jumbo coding I came up with this which seems to work fine:

<?php

$cat_args=array(
'orderby' => 'name',
'order' => 'ASC'
);
$categories=get_categories($cat_args);
foreach($categories as $category) {
$args=array(
'showposts' => 50,
'category__in' => array($category->term_id),
'caller_get_posts'=>1
);
$posts=get_posts($args);
if ($posts) {
echo '<p><a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name.'</a> </p> ';
foreach($posts as $post) {
setup_postdata($post); ?>
<p><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></p>
<?php
} // foreach($posts
} // if ($posts
} // foreach($categories
?>

The above code successfully displays all my categories and their respective posts under each one of their names.

This goes inside the loop under the <?php if (have_posts()) :?> for those who know Wordpress.

Next what I want to do is basically adjust this to an accordion menu I've written. The accordion HTML is pretty simple:

<div id="basic-accordian">
<div id="test-header" class="accordion_headings header_highlights">Category 1</div>
<div id="test-content">
<div class="accordion_child">
<ul>
<li>Post 1</li>
<li>Post 2</li>
etc
</ul>
</div>
</div>

<div id="test1-header" class="accordion_headings">Category 2</div>
<div id="test1-content">
<div class="accordion_child">
<ul>
<li>Post 1</li>
<li>Post 2</li>
etc
</ul>
</div>
</div>
</div>

So what is needed from what I can tell with my less than basic knowledge of PHP is that the name of the Category needs to be wrapped with the <div id="testX-header" class="accordion_headings"> CATEGORY NAME </div> where X = ascending number, 1, 2, 3 etc, and wrap the <div id="testXcontent"><div class="accordion_child">..posts..</div> around the actual posts of each category.

This is probably done with a simple 'for' class or something? I have no clue, I've been troubling about it for 2 days now and can't seem to be able to arrive at a working solution on my own.

Any help is much appreciated.

*bump*

anyone?