cjrgreen: See, that key is tied to the original hardware. It has already been activated with that hardware. It's not automatically usable with different hardware. Windows knows what hardware it is running on and checks whether the key was activated with this hardware.
So, you try to come up on new hardware. Windows sees that the hardware has changed and says, in effect, "no, this isn't the computer I was installed on." It tells you to activate again. You try to activate automatically online. Microsoft's server sees your product key and says "I've seen you before. You activated on a different computer. I won't activate you again."
It tells you to go to Microsoft for a new activation key. You need
both the product key and the activation key. Since you couldn't get the activation key automatically, you have to talk to a tech support rep to get one.
You call Microsoft, tell the tech support rep that you had to replace the motherboard. The tech support rep gives you a hard time about it, then gives you a new activation key.
You type the activation key into the Windows dialog that wants it. And everybody's happy. That's all there is to it.
That's mostly correct, but if you don't boot the copy up for at least 120 days before you install it on new hardware the activation will basically time out and allow an installation on different hardware without calling tech support.
But, unless the OP happens to have multiple copies or is extraordinarily patient calling is probably the best choice.