You moved it. You didn't copy it.
Don't go breaking any laws now - but that's the way for the computer's OS not to detect hardware changes and trigger re-activation.
Ok, but what if you already messed up?
The online activation will not work. There's a lot of cases and it depends on your license and ... - but if you're doing perfectly legal things you have all the right to run your machine and not have to sit on the phone with Microsoft.
What you want to do is shut down the machine, move it back to where it was originally activated. Turn it on and this time it will activate properly online. Now shut it down and move it back to where you had problems. When you get that dialog: You moved it. You didn't copy it.
There's a gotcha there, and that's what this blog is all about.