This may be a silly question, but do you have WiFi enabled on your Nook? It is hard to tell when you say, "I have gone over to B & N and tried "purchasing" several free books by signing in" if you mean using a computer and browser or you mean using your Nook.
If you mean you went to their WEBSITE with a browser and purchased a book, you then need to use your Nook with WiFi enabled. In fact, when you turn on your Nook and WiFi, the book should appear in your library without doing anything, usually, if it is a book you earlier purchased via a browser.
The best way to buy a book from B&N is using your Nook from start to finish, using Shop.