You've got some serious HTML-formatting issues on the page that are probably "interfering" with the auto-submit javascript for the check/moneyorder and PayPal payments, starting with a stray ending } somewhere within your template's html_header.php.
Code:
<script type="text/javascript">window.jQuery || document.write(unescape('%3Cscript type="text/javascript" src="//code.jquery.com/jquery-1.11.1.min.js"%3E%3C/script%3E'));</script>
<script type="text/javascript">window.jQuery || document.write(unescape('%3Cscript type="text/javascript" src="includes/templates/responsive_sheffield_blue/jscript/jquery.min.js"%3E%3C/script%3E'));</script>
}
and continuing with the fact that your </body> tag comes before a collection of <script> and <meta> tags coming from (I'm guessing) the template's tpl_main_page.php.
The banner's display can be corrected by your editing of /includes/modules/pages/checkout_one_confirmation/jscript_main.php, adding the highlighted code fragment (I'll book that change for v1.0.5 of the plugin):
Code:
if (!$confirmation_required) {
?>
$(document).ready(function(){
$('body', 'html').css({
"overflow": "hidden",
"height": "100%",
"background": "none"
});
$('#navBreadCrumb, #bannerSix', '#bannerOne').hide();
$('#checkoutOneConfirmationLoading').show();
$('form[name="checkout_confirmation"]').submit();
});
<?php
}