You would have have a DNN Installation running (with Forum Module installed and configured) and then you could use iframe with a SQL query parameter to pass the users log-in details as long as the log-in details was same for both application for both users.
But I think NINA is totally correct in suggesting that this would be a waste of time. Why don't you set up a portal working on you URL as a sub-domain and then redirect it when they click the forum button.
You can always use a skin that reflects your sites colours.
Or better yet build your whole website with DNN using one on Nina's great designs, would be a well worth time spent