Drush enable module | not working | Drupal 7 on WAMP with PostgreSQL
I'm not on Windows or using postgres today, but I can suggest how to debug:

What you've got right now is that your cli environment seems to be failing to connect to the database correctly.
Checking your database-level access from drush, using verbose (-v) debug (-d) feedback may provide clues.

For instance, given your current failure, I would run 

  drush -v -d sql-cli



that will, among other things, show you the exact database connection command being attempted that is failing. 


You can then copy that yourself, run it again,  and see what variations of that
   command will and will not work. One of the more common issues seems
   to already be covered (the difference between 'localhost' and
   '127.0.0.1' depending on installation and version issues. There may
   be other issues such as 'cannot locate postgres.exe in the current
   $PATH' or whatever.

This is not an answer to the question, but a suggestion on how to get clueful when a (any) drush command just doesn't work. You can also use the -vd flags on your 'en' command, though I don't know how conclusive the feedback you get there will be.