Offset Loop by 1 , Limit next loop to 1 (Most Recent) Post

Neither of those are complete loops. That is, in both you have the start of an if but not the end of it, and the start of a while loop, but no the end of it. Also, you shouldn’t be using query_posts either, as it over writes the main query and is rarely the right function for pulling posts. get_posts would be better.

I would do this, using one as an example:

<?php $r = get_posts('offset=1'); 
    if ( !empty($r) ) : 
        foreach  ( $r as $post ) : 
            setup_postdata($post);
            // stuff
        endforeach;
    endif; ?>

That should solve your problem with the page not loading.

What you are doing can be done with a single loop though, since get_posts without the offset will pull everything. You just need to take the first element as the recent post and loop through the rest.