I love this plugin and hope we can work this out.
I've been using Contact Form 3.8.1. However, I updated WordPress to 3.9.1 last week and suddenly the Contact Form did not show up on my site. In addition, it seemed to break the </div> tags and caused the remainder of the page to render incorrectly. I replaced 3.8.1 with 3.8 and everything worked again.