Also, have you found his arrival in the United States in the ship passenger list? It may or may not give you some idea of where he came from in Denmark or who traveled with him.
Once you have a pretty close arrival date, there is a good chance you can find him in the Copenhagen emigration database. That usually gives you a pretty close place of last residence. If he was older than 10 when he came to the U.S., you will then have a pretty good chance at finding him in the Danish census. Starting around 1845, the Danish census will tell you what parish he was born in.
Danish location categories are just getting started. Mostly we are in the research stage waiting our turn and hoping Aleš can create a lot of what we need with his programs. Meanwhile, I and a few others are creating the sogne (parish) categories and linking them to the category tree as needed. Let me know when you get some idea of where in Denmark and I'll get them set up for you.