I had similar problems integrating WordPress into my site. Had to write a horrible auto-loader which maps WordPress class names to their respective files. WordPress sometimes has multiple classes in the same file so it wasn’t straightforward.
The WordPress globals and constants need to be registered next, so adding the following before making any calls to WordPress seemed to do the trick:
require 'blog/wp-config.php';
You should then be able to add the following code on your page:
<?php
define('WP_USE_THEMES', false);
require('/the/path/to/your/wp-blog-header.php');
?>
