Windows 8.1 activation on HP Pavilion Touch 14-N009LA throws error 0xC004F074

My sister has an HP Pavilion Touch 14-N009LA that came with Windows 8. This computer was upgraded to Windows 8.1 once put into service, but since I'm not the owner of this computer I don't know if Windows updates were enabled on this computer, though it does have an antivirus (a Telmex-branded version of McAfee) and an antispyware (Spybot S&D).

As it turns out, the Windows installation on this computer was never activated, and we only noticed because my sister tried to install Windows 10 and the upgrader complained about Windows being not genuine. When I try to activate it, the Windows activation dialog throws an error 0xC004F074 that says something along the lines of "Could not contact any key management service (KMS)" (the error message as it appears on my system is in Spanish: "No se pudo establecer contacto con ningún Servicio de administración de claves (KMS)").

I already tried running sfc /scannow, and while it did turn up a corrupted system file that I had to fix with this Sysnative system file fixer, after fixing that file the Windows activation dialog still couldn't activate Windows. I then ran sfc /scannow again and this time it didn't turn up any corrupted system files. I then ran the antivirus and antimalware to see if something was bugging my sister's Windows, and while Spybot SD did remove a SearchProtect malware I still get the same error. I cannot use slui 3 because my computer didn't include any such thing as a printed product key (it's apparently embeeded somewhere within the Windows installation). All I ended up finding was this HP support forum thread that has no answer and is full of people complaining. This doesn't seems like a model-specific issue, however, because as it turns out both a friend and I have each a specimen of the same laptop model, and Windows activated just fine on each of our own laptops.

Is there any other way I can fix this activation error?