Loop Problem: Displays same set of post for all categories

You are passing the same arguments to retrieve every set of posts. You have alter the arguments dynamically to reflect the current category.

$categories = get_categories($catArgs);
if($categories){
    foreach($categories as $category) {
        $postArgs['cat'] = $category->cat_ID;
        $my_query = new WP_Query($postArgs);
        // ...

Untested, and I am away from my dev server but that should be pretty close. You will have overlap for recent posts if several show up in multiple categories and I would suggest passing an ignore_sticky_posts argument to WP_Query as well.

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