I suspect you didn't call Microsoft at all, but one of the bogus numbers from sites claiming to be able to provide Office etc support.
Transferring Office to another PC is quite straightforward - simple re-install it from the original installation media or, if you obtained it via a download, from your backup copy of the download. You'll need the product key, but you should already have that; if not, you can retrieve it using the Magical Jelly Bean KeyFinder:
http://www.magicaljellybean.com/keyfinder/