Boot to Safe Mode with networking and try this MS Fixit:
SM with networking will rule out interference from 3rd party software
[security-related software] and *usually*, will allow the installation
of required software components needed to update.
Suggest you download and save the fixit [ResetWindowsUpdate.msi], close
the browser, and then run it.
If the Default run does not resolve the issue, run it again in Agressive
mode while still in Safe Mode w/networking.
The system *must* be connected as ResetWindowsUpdate will download the
latest release of the Windows Update Agent.
Reboot afterwards and see if the system can update now.
> A crossreference,
> Most important is that people do find the error 0x8007007F when they
> encounter it on the Windows Update Site.
> (p.s.: the link might need an extension)