‘Invalid post type’ breaks backend

I updated https://workio/insight/ to WP 3.3.1 soon after it was released and everything worked fine until yesterday night when I tried to add a new post.

The problem
On every link in the backend in the ‘Posts’ section I get an empty page which says ‘Invalid post type’. Only adding a new post brings up the Editor and most options, but not the save/publish box. Screenshot: https://skitch.com/lucahammer/garye/add-new-post

I am still able to add new posts through Quickpress on the Dashboard.

What I tried
I didn’t use any custom post types and after trying some related solutions I found on the ‘Invalid post type’ error, which all failed to work, I deleted everything from the wp_posts table except the one post already published. The post type of this post is ‘post’.
I turned all plugins off.
I used the default theme.
I tried a different browser.

After several hours of testing different stuff I come to you to ask for help. If you have any ideas how to solve the problem, I would be really thankful. Else I will have to ask one of the devs to reinstall WP (I got no server access).