No, you can use the copy you have (if it is a full version). Most vendor versions (Dell, HP, Compaq) are not full versions, and won't work on a different system.
Since you are reinstalling it, and not just putting it on an additional computer, you are in the clear legal-wise. Actually, you could use a different Windows CD as long as you use the code that came with the Windows on your current system (if you don't have a full version).
Windows takes a snapshot of your system. When you boot, it checks what it finds against what it knows. If the two doesn't match up, Windows won't boot. Changing mobos is a major change, and Windows will see it.
My Rig: SABLE
Antec 300 Illusion / Antec EarthWatts EA650 650W / EVGA GTX 760 2GB
AMD FX 8320 x8 Black Edition / Gelid Tranquillo / MSI 970A-G43
Sandisk Ultra Plus 128GB / Samsung 840 120GB / WD Black 750GB / WD Green 1TB / WD Red 3TB
G.SKILL Ripjaws 2x2GB DDR3 1600 - Crucial Ballistix Tracer 2x2GB DDR3 1600
Win7 Ult 64-bit - Func MS3 Mouse - CM Storm QuickFire Rapid Mech Keyboard
R.I.P. Danny L. Trotter
... 14 Nov 1945 - 4 Sept 2009