I suggest powering you nook on and off fully. Then check to see if it's there. If not, it may take a while. Or it could be your wifi. Mine took about 1 afternoon one time when I bought the book from the computer. I am sticking to buying books from my actual NC now.
And please make sure you're downloading right. Use the Wi-Fi on the Nook to purchase books, etc. Even if your downloading a "free" book, hit the download button. This "buys" it. Then go to your Nook Library & hit the download button again. Sometimes it can take a full 24 hours to download something. This happened to me when I downloaded a free, "Read To Me", children's book. Last night I downloaded a free, regular book, & it appeared on my Nook in 10 minutes. So it just depends. Hope you get your books to download.
they just won't download. one just doesn't do anything and the other 2 show they are downloading but never do?
settings > device info > erase and de-register
make sure you still remember your wireless network password and your B&N accounts password