|What microsoft account is it asking for/when does the request appear? Are you trying to network the two computers together?|
The windows product ID is pretty much meaningless. It's generated when windows is first installed and is displayed in lieu of the product key. I can't think of any reason it would ask for either the ID or key in relation to your problem so it must be looking for something else.
Don't forget to preorder your Hatch green chili for this fall. Many vendors ship world-wide.