Multiple loop issue – pull one featured and then continue the loop

Replace $do_not_duplicate = $post->ID; with $do_not_duplicate = get_the_ID();.

After the first loop (the featured) call wp_reset_postdata();

....

</div><!-- end #featured -->
<?php 
endwhile;

wp_reset_postdata();

if( have_posts() ) : while ( have_posts() ) : the_post(); 

...