After I upgraded to Drupal 7.41 from Drupal 7.39, my site went down and I got a 500 internal server error message. What's more frustrating is the fact that there were no logs whatsoever.
I checked Drupal and Apache logs and no errors were to be found. After a bit more digging online, I figured the solution was rather simple and it was silly to not have thought about it.
I used Drush to upgrade the core and some modules. While upgrading, the .htaccess file has been overwritten. Luckily, drush takes a back up of your site before doing upgrades.
I restored the original .htaccess file from the drush_backups folders and the site came back (whew).