From the new site:
Yes, all discount codes provided by previous version of the Nine Inch Nails store will be good for a single use in the new store. If you run into any problems with your code, please write in to us here and we'll be happy to look into it for you.
They also have a form to fill in if you "have an unfulfilled order from a previous store" : https://nine-inch-nails-support.zend...previous-store (!!)

Let's see where that takes us...