Template Changes to Default After Update

Have you try:

– Check the error logs on your server for a more specific error message. If you need help locating them, ask your hosting provider to help you with that.
If the issue is happening very early in the loading, it may not get to WP debug. That’s why the server’s error log would be a better place to look.
-deactivating ALL plugins temporarily to see if this resolves the problem. If this works, re-activate them individually (one-by-one) to find the problematic plugin(s). If you can’t get into your admin dashboard, try deactivating via FTP or SFTP or whatever file management application your host provides. If applicible, also remember to deactivate any plugins in the mu-plugins folder. The easiest way is to rename that folder to mu-plugins-old.
– To rule out any theme-specific issue, try switching to the unedited default theme for a moment using the WP dashboard. If you don’t have access to your admin area, you can switch to the default theme by renaming your current theme’s folder in wp-content/themes and adding “-old” to the end of the folder name using via FTP or SFTP or whatever file management application your host provides. Alternately, you can remove other themes except the default theme. That will force your site to use it.
– resetting the plugins folder by FTP or PhpMyAdmin. Sometimes, an apparently inactive plugin can still cause problems (because the hooks remain unless plugins completely removed or some plugins stick around in cached files. So by renaming the folder, you break them and force them inactive).

The TwentyThirteen theme also shows nothing with all other plug-ins deactivated

How about Twenty Twelve theme with all other plug-ins deactivated?