or, if you decide to change motherboard, you can simply call the 800 number microsoft provides you, tell them you are only running this copy of windows on one machine, and they will provide you with an activation code.
What about using a HDD from different system with a new computer and reactivating the formers win7 with the new OEM key? Is that too convoluted?
You may be able to do this, but you'd be better off doing a clean install anyway due to issues you may have with the machines being different(hardware-wise). Most people will recommend doing a clean install on a system rather than moving the OS drive over - and this recommendation has nothing to do with licensing.