Thank you, HairyFool.
I indeed found xxx-6P6GT key on the Win 7 notebook (though I think it's a 32-bit key and I see another key there which ends in xxx-xxVP7 (maybe because this is 64 bit?)).
In any case, if I did install Win 8.1 Pro on this computer using the supplied DVD, which key would it use then? I assume it could not be those generic Win 7 Pro keys since those are specific to Win 7 Pro.
Since BIOS has that tag you mentioned, would I be able to then upgrade to any Windows version in future without any key? (That seems unlikely)
If I were to install Win 8.1 Pro upgrade using the supplied DVD, it would also use some generic common key, or would it be a unique key for me?
If it's a unique key, is there some way for me to find it without installing the Win 8.1 Pro by reading it from somewhere?