If the drives are similar (examine the connectors carefully) the system should boot -- but Windows may suspect you have cloned a copy of the operating system if it detects a significant hardware change like that.
You may need to ask Microsoft's permission to use your computer with your new drive in (!).
If you get over that hurdle or are prepared to reinstall the operating system, it should be fine.
If you have to talk with MS to get the OS to work, since you had a motherboard failure you should tell them that it failed and you had to install a new motherboard.
If the new motherboard is similar enough to the old motherboard then it might work, and eventually change out any drivers that it needs. If there is too much difference in motherboards it might not even boot. I've not had too much trouble doing this with much older versions of Windows but haven't needed to do it recently.