Upgrading to WordPress 3.7.1 broke a lot of backend (admin, wp-admin) pages. I got 404 Missing and sometimes 500 Internal Server Errors for themes.php, and options.php. No quick fixes were working…
Upgrading PHP from 5.3 to 5.4 solved all issues.
WordPress.org states that the minimum PHP version required is version 5.2.4 or greater. I was using 5.2.11 and upgraded to 5.3.15. Good luck!