I had exactly the same problem – don’t know why its happening – all works fine on a local server too.
However, I’ve hacked it to work. May not be elegant but it works.
At the top of the page (approx line 10)I added this line
$bugfix=ABSPATH."wp-content/plugins/wp-contact-form/";
so wordpress knows where to find the plugin
and on line 27 changed
include('buttonsnap.php');
to
include($bugfix.'buttonsnap.php');
Seems to work fine now.