Why are array_slice() and array_chunk() not working?

You need to do the slice on the results, not the arguments to the function. So:

$arr = array(
    //$section_top_parent is the top parent of the custom post type "section"
    'child_of' => $section_top_parent,
    'post_type' => 'section',
    'title_li' => NULL,
    'depth' => 1,
    'sort_order' => 'asc',
);

$result = wp_list_pages($arr);
$sliced = array_slice($result, 3, 5);
wp_list_pages($sliced);