Sounds like microsoft changed the danish layout.
The behaviour you want is called "dead keys" and the layout knows which keys should work like that.
If you want the old behaviour back, you need to do the following: Download MSKLC (Microsoft keyboard layout creator) from microsoft's website, install and open it and then go to File->Load existing layout and then select the danish one.
Then double click the accent key to open the popup, which includes a checkbox to make it a dead key.
Then compile and install the layout. I don't remember where exactly that button is but you'll find it. If it doesn't work first try, make sure that you change the name of the layout on the second try. Windows is a buggy mess and if you reuse names, it will break sooner or later and you'll find yourself with layouts that cannot be removed anymore.
You can also set a few other things in the layout like shiftlock, but as I said windows is a buggy mess so doing that will almost certainly break something.