what are the signs that a check disk/disk repair is not working?
Seems like the OS processes are having issues to start correctly.
Please try this:
Start your system and wait until you get the black screen with only the mouse cursor moving.
Hit Ctrl + Shift + Escape to get the task manager.
Once you get the task manager, click on File menu button and select Run New task
The task to Open is "explorer.exe" and hit OK.
This should force the system to start back up the explorer process and show you your computer desktop. If so, go ahead and save your data and proceed formatting the HD and installing Windows again. Don't recommend recover or reparing tools at Windows 10.
If your user desktop didn't come up, look for another computer and save your data putting the HD as an slave in another system via USB with an adapter or SATA cable if there is a Desktop computer.
This happens often after Windows 8 update to Windows 10 without reinstalling or Windows 10 being turned off without advise.
Hope this helps you to find a way to solve your issues.
Regards,
Luis