Whatever that string is (which I see you've deleted from your post), it's not an Office Product Key. I suggest you download a copy of the Magical Jelly Bean Keyfinder (a freeware utility that retrieves your Product Key) from:
http://www.magicaljellybean.com/keyfinder/ and run it on one of the PCs that already has Office installed & activated, so as to retrieve the correct Product Key.