Possibly...but maybe not.
Activation of Windows is, at times, unpredictable. Legally, MS says that a change of motherboard is a new system...and only retail licenses are supposed to be able to move fron System 1 to System 2...but there are situations where what is legal is not what necessarily is the verdict by the folks at Product Activation.
I find that...when it comes to PA, you don't know until you try.
If the motherboard is bad...that may have resulted in damaged files on the hard drive. Such files may prevent/impede any effort to run Windows properly.