The most likely problem it's a driver that, most likely because of a bug, has reported a different hardware id to Windows.
There's nothing you or us can do: the hardware change is entirely a black box for us, we don't even know exactly what Esellerate checks to trigger an hardware change, and we won't even dare try doing hardware change detection with our own code, because it's just too complex to always work reliably (as you can see...), because of driver bugs.
The other issue, the activation window covered by your browser, can be easily prevented by going into Windowed mode during the activation, so you can freely move all windows on the screen.
And, you are not even SUPPOSED to see an activation window. Normally, you should only see a button to confirm your activation, and that's it. Nothing to type and surely no internet browser to use. What you are seeing is the OFFLINE activation, which comes out if your internet connection is down OR if you have a firewall that is blocking online access to the activation servers.
So, to make the reactivation easier, be sure you turn off your firewall, so there will be nothing to do, other than pressing the OK button.