Drush update for the first time hosed my website
Probably one of the updates of your modules is messing up. Most recently I had this problem with updating Rules which broke my site the same way it did yours (WSOD).

Reverting and updating one by one can show you what went wrong.

If you use drush you can do: drush up modulename (e.g. drush up rules) to update one by one, instead of drush up which updates everything. drush up drupal only updates core.