I tried my idea first of enabling the admin account and a normal mode cmd.exe shell and it ran dism ... /restorehealth successfully
However, the total upshot seems to be that I can now run eventvwr in normal mode rather than safe mode only. Task Manager still won't start.
In an attempt to allow other users to log in and get an explorer shell and keep the administrator user on a cmd shell, I inadvertently get a situation whereby a test user got a File Explorer window rather than the explorer UI. I then got the idea of starting cmd.exe via explorer but explorer hung the moment I tried to access C drive.
I'm fairly sure C drive is OK as I ran chkdsk /f /v /r on it and nothing alarming cropped up.
I think I ought to pull the trigger on a clean install as I'm running out of ideas and I've got little to go on (I'll have another trawl through eventvwr to see if I can spot anything to act on). Weirdly though, the customer previously gave the go-ahead for a clean install "if I have to", then when I rang them this morning to keep them updated with progress, they asked me to ring them before doing a clean install. Maybe they want some extra reassurance first, e.g. yes I've backed up their data.
I wonder if I could run transwiz on the main user's profile with Windows in this borked a state, as it would surprise me if anything is seriously wrong with the profile data considering how Windows is acting to any user attempting to log in with explorer as the shell. Managing to grab the user profile and drop it on a new install would help the customer get back on their feet with this PC quicker.