So it seems that using $wpdb is out of the question, as is creating a second $wpdb object to handle MS-access.
Still you have php files which do handle MS-access, I see no reason why this code cannot operate within the WordPress framework.
I understand that you have tried to use file include, but to no result. I think that this approach is worth pursuing. Enable DEBUG messages (temporarily) in your WordPress by editing your wp-config.php so that the WP_DEBUG setting is true: "define('WP_DEBUG', true);"
It would be best if your function DID NOT echo anything, but rather returned its text to be displayed as text strings, this will give you greater flexibility in how the display happens and where. Using shortcodes is likely to be useful, details here:
http://codex.wordpress.org/Shortcode_API
