Notebook Boot and Lockup

Hi there. 

Earlier this week my wife woke up to find her laptop had restarted overnight (possibly thanks to a Windows update, I'm not totally sure) with the blue Automatic Repair screen and the message "Your PC did not start correctly" and will no longer boot into Windows 10 (1709)

She'll get the spinning circle at the HP splash screen before the computer blinks off then comes back on with Preparing Automatic Repair. We then get the options to either Restart or Advanced Options. Selecting Restart just starts the process all over again. If I go to Troubleshoot > Advanced Options here are my options and what happens:

System Restore: "No restore points have been created" (I know she had at least one before this incident but it's no longer showing up)
System Image Recovery: "Windows cannot find a system image on this computer"
Startup Repair: I get "Diagnosing your PC" followed by "Checking disk for errors" then finally "Startup Repair couldn't repair your PC"
UEFI Firmware Settings: This takes me to the DOS-type Startup Menu (F1 - System Information, F2 - System Diagnostics, etc)

Command Prompt: This will work and takes me to "X:\windows\system32>" by default
Go Back To Previous Version: "We ran into a problem and won't be able to take you back to the previous version of Windows"
Startup Settings: None of the options in here make any difference - the computer does the same 'failed start' followed by Automatic Repair (which again, continually fails).

Also, I CANNOT boot into Safe Mode.

I've run the HP Diagnostics and every single test has passed without a problem. I also ran Chkdsk and sfc scannnow, which both found no problems.

The Startup Repair logfile tells me that each test completed successfully and ends with:
"Root cause found:
-------

Startup Repair has tried several times but still cannot determine the cause of the problem"

HP Recovery Manager : These options give the same results as previous methods above.

I've also used DISM via the command prompt to apply the kb-4073290 msu, which has made no difference. 

Is there anything I can do to make Win10 start again? We really don't want to have to do a repair installation since my wife has installed quite a lot of programs over the years and (despite my continued insisting) hasn't run a backup or created Restore discs. If we DO have to go down that road, I know we'll lose any programs she's installed, but will we also lose any folders created on the C: drive?

EDIT: I'm able to use the Command Prompt to open up Notepad and browse folders & drives, which suggests that Windows is at least partly running, right?

Thanks for any help.