Using t() with langcode in Drupal 7
The string (first parameter) always needs to be in English, from the Drupal 7 API:


  $string A string containing the
  English string to translate.


The langcode just means that the string will always be translated to Danish, no matter what the active language is. So if you'd be surfing the French site, you'd see the Danish string.

I'm afraid you'll have to translate your Danish strings back to English strings.