Can't enable Windows time service (Windows 10) - Access is denied even to Administrator

My W10 computer is unable to sync time (sync failed). I found that the time service is not running.

When I try to start it, I get "Access is denied" - even in an Administrator shell:

C:\WINDOWS\system32>net start w32timeSystem error 5 has occurred.Access is denied.

There are many help articles on this, but the first thing they always say to do is:

w32tm /unregister

Which also results in 'Access is denied (0x80070005)'.

For that matter 'w32tm /register' generates the sameerror too.

So any answer that says to stop the time service, unregister it, and register it again will not work as access is denied for those operations also.

How do I get the time service running?