Can't login: user/login redirects to index page
Do you have drush installed? I would try clearing cache as a first step, probably won't fix it but worth a shot. After that try renaming the theme that you are using to force Drupal to use a different theme, or change the theme manually in the database. Try disabling modules one by one to see if any of them might be interfering. Start with any module that changes paths (like PathAuto...). I also noticed that no matter what your site will not throw a 404 page not found error. If that was intended, then whichever process you used to redirect 404's to index.php could possibly be causing an issue.