You could try replacing:
<div id="menu">
<ul>
<li class="page_item <?php if ( is_home() ) { ?>current_page_item<?php } ?>"><a href="<?php bloginfo('url'); ?>"><?php _e('Home', 'elegant-grunge') ?></a></li>
<?php wp_list_pages('title_li=&depth=1'); ?>
</ul>
</div>
with:
<?php wp_page_menu('depth=1'); ?>
But you'll need to go through your stylesheet changing every reference from #menu to .menu.
If that doesn't appeal, make a note of the id for the page you're currently using as your Home page, then amend:
<?php wp_list_pages('title_li=&depth=1'); ?>
to
<?php wp_list_pages('title_li=&depth=1&exclude=X'); ?>
where X = your home page id.