Drush 6 on Windows not doing anything
Figured it out. It was a problem with the reverse-proxy we're using. I installed a different version of drush in cygwin and tried to run it. Here it paused like I described above, but after a minute showed me this error:


  Drush needs a copy of the PEAR Console_Table library in order to function, and the attempt to download this file automatically failed.
  To continue you will need to download the 1.1.3 package from http://pear.php.net/package/Console_Table, extract it into C:\cygwin64\usr\local\src\drush/lib directory, such that Table.php exists at C:\cygwin64\usr\local\src\drush/lib/Console_Table-1.1.3/Table.php.


I installed this package manually and now things are working. I just didn't realize Drush was trying to download extra content.