This error can occur if you’re using WordPress on an external web site.

WordPress recommend using the following code;

<?php 
/* Short and sweet */
define('WP_USE_THEMES', false);
require('./wp-blog-header.php');
?>

However. To fix your NetworkError: 404 Not Found error try using the following code;

<?php
/* Short and sweet */
define('WP_USE_THEMES', false);
require('./wp-load.php');
?>