This is indeed an "interesting" issue...
The fact that the letters printed on your keyboard and the letters printed on the screen do not match may simply indicate that the keyboard "map" has been changed and that Mac OS X does not recognize your keyboard as Danish any more.
Therefore, the first thing to do would be to have a look at the "International" preferences pane, available through the "System Preferences" application. Then, click on the "Input Menu" tab and make sure that only "Danish" ( or the appropriate keyboard map ) is selected.
Let me know if this helps !