I have still my old laptop functioning, so I'll give it a try and use this tools on that machine, with some luck there is some trace of the activation key yet.
One thing we need to do when (if) MS support solve this problem is to recover that activation key and save it on three different location to be safe. I mean, if this is the path we have to walk through every time a bios update is available, this is something to consider... just in case