I've been going crazy trying to figure this one out, and I thought I'd share my solution now that it's resolved. I recently moved to a new server, and I noticed that I couldn't delete posts or load certain pages in the WP admin panel.
If I clicked "delete" in the Manage Posts screen, nothing would happen. If I edited a post and clicked the "delete post" button, I would get a blank white screen, with http://www.my-site-dot.whatever/wp-admin/post.php in the address bar. In other cases, the browser would try to download the post.php file.
I went so far as to tweak my server's php.ini settings, but none of that had any effect.
The problem turned out to be that I had two plugins called runphp.php (one was runPHP.php - case-difference only). Only one of them was activated, but this was causing the problem.
I deleted both plugins, re-uploaded a fresh copy of the plugin, reactivated it, and all is well. Hope someone, now or years in the future, finds this useful :).