How do I get an archived book back onto my nook app on my windows tablet
Short answer: un-archive it.
One way of doing this via the website is:
1) in your browser go to: http://mynook.barnesandnoble.com
2) Sign in using your B&N account.
3) Click on the Go to Library link
4) Select the option to show archived items.
5) Click on the Move to Active link for the book you want to restore from archive.
6) On your tablet, refresh your library display, download, and read your book.
It is probably possibly to do all this from your tablet more easily, but since I don't have access to a windows 8 table I am unable to give you specific instructions.