You are referring to the navigation menu. This is generated by the code between <!--bof-navigation display--> and <!--eof-navigation display--> in the code you posted above.

To move it, you would take all the code from <!--bof-navigation display--> to <!--eof-navigation display--> inclusive and move it to where you want it to go, which by the sounds of it would be just after the following code
<?php require(DIR_WS_MODULES . 'sideboxes/search_header.php'); ?>

</div>
You will probably need also to tweak the CSS for these areas to have them display nicely together.