This would remove the entire header on a specific page
<?php
$pageid = null;
if( is_home() && !is_front_page() ) {
$pageid = get_option('page_for_posts');
} else {
$pageid = $post->ID;
}
// replace number with id where you don't want it shown
if ($pagid != 1234) {
?>
<div class="header-default-top-section">
... the rest of your header code here
<?php
}
?>
