The key is linked to both the case and the motherboard, although only the motherboard makes any difference. You are violating the eula if you use another motherboard, even if you do not reinstall, however I very much doubt you'll ever have a problem with that. To re-register the product I believe yuou kust phone microsoft and explain the situation and they'll re-activate the code for you.
Never swap out the motherboard for another and not reinstall unless they are exactly the same board (even the same chipsets will use different hardware, such as networking and sound) as it camn cause multiple problems such as new devices not installing and general instability.
