I tried reproducing the problem on a site with only one page, no posts.
It worked: the form was displayed properly:
http://i.wpne.ws/Yt5v
I was able to submit a form as well, and received an email immediately.
Form appear as simple text: [Contact form].
Could you let me know how the contact form shortcode looks like in the page editor? It should be something like this:
[contact-form][contact-field label='Name' type='name' required='1'/][contact-field label='Email' type='email' required='1'/][contact-field label='Website' type='url'/][contact-field label='Comment' type='textarea' required='1'/][/contact-form]