After upgrading/updating wordpress to 4.4, I could not log into the admin area. It kept giving me a permanent redirect loop. I spent quite a while pouring over possible fixes, and ended up with the following:

In FTP, make sure all the top level files are 644 permission. These are the files directly under the wp-admin folder. This allowed me to log in properly.

Since the front end of the site seemed to be working properly, I had not gone through every page, but later found that any page with a permalink was down.

To fix this, I went into the settings and into permalinks and just saved what was already there. This saving of this setting fixed the front end.

This WordPress 4.4 upgrade/update broke the entire site. Ugh! Hopefully this helps you fix yours!