Outputting main menu in full in page.tpl.php
Calling menu_navigation_links() with only the menu name by default provides only the top level links.  To delve deeper you need to provide the second $level argument, eg:

$main_menu =menu_navigation_links('main-menu', 1);


will provide the top and next level links, and:

$main_menu =menu_navigation_links('main-menu', 2);


will provide one level deeper.