Sorry. Posts are getting crossed here.
I'd start by commenting out this line:
<?php if ( get_theme_mod( 'cat_nav' )) { wp_list_categories( 'title_li=&depth=1' ); } else { wp_list_pages('sort_column=menu_order&title_li='); } ?>
... and replace it with my own list of links. Something like:
<li><a href="permalink/of/first/page">First item</a></li>
<li><a href="permalink/of/next/page">Second item</a></li>
<li>...</li>
Then I'd have a look to see what I've messed up :-)
I would very, very strongly advise you to do this in a child theme. See:
http://codex.wordpress.org/Child_Themes
Child themes take about 5 minutes to create and can save you no end of grief later on.
When you have a child theme, copy the parent theme's (Garland's) header.php file into your child theme and start making changes. Make sure you keep detailed notes of the changes you are making and that you have backups of any files you change.
Oh! And a link to your site would make it much easier for us to give you useful help.
HTH
PAE