Now, as for the Danish room mate, he might as well have been speaking Greek.
Danish is if anything ever so slightly closer to German in vocabulary and grammar, but the pronunciation is another matter.
The effect is bigger in writing. In high school I worked my way through Faust in German by finding an old Danish translation as a parallel text - the old Danish version was a decent halfway point when I struggled too much with the German, and helped me find similarities I wouldn't otherwise.
Case in point:
Maybe I should throw that into the language somewhere.