hello carel, it seems that the javascript is completely broken on your site, i see this :
Resource interpreted as Script but transferred with MIME type text/html: "http://www.teurlings.biz/NO_HACKERS_ALLOWED.php".
your vhost or htaccess probably disallows to load cached javascripts from the cache directory:
<script src="http://test.cp-papierwaren.nl/cache/com_onepage/opc_dynamic_nl-NL_bb3437fcc0df00bcc82d5c92ea0a68c8.js" type="text/javascript"></script>
please disable this feature within opc's general tab bottom:
please consult this issues with the security software that you are using.
i also suggest an opc update to the very latest as we had recently fixed a few php5.3.x related problems that you may encounter and maybe related to the shipping as well. (but your installation does not load shipping because it's set to "delayed" and no ajax is working on none of the fields -> maybe a widgetkit unsets the javascript listeners)
best regards, stan