When I try to use Snipping Tool I get a message stating that "The Snipping Tool is not working on your computer right now. Restart your computer and try again. If the problem persists, contact your system administer."__What can I do to fix this?__Thanks

I restarted in Safe Mode.  I tried updating the registry... same result.  I tried running Snipping Tool... same result.

I do not have MS Office on this system. Is it required?  It doesn't seem that it should be as Snipping Tool comes with Windows 10 proper.

I take it you used the "Run as Administrator" option?  If so then you are being stymied by the "Some keys are open by the system or other processes".

You could try from Safe Mode to see if you can amend the Registry.

Start your computer in safe mode

http://windows.microsoft.com/en-au/windows/start-computer-safe-mode#start-computer-safe-mode=windows-7  

How to start Windows 8, or 10, in Safe Mode

http://www.bleepingcomputer.com/tutorials/start-windows-8-in-safe-mode/

Incidentally does the Snipping Tool work in Safe Mode?

Unfortunately, no dice.  I was able to located regedit.exe in c:\windows and I get the same message upon importing.

See if you can locate Regedit.exe here, C:\Windows.  When you locate it, try right-clicking on the actual Regedit.exe and selecting the "Run As Administrator" option?  Do so even if your user is an Admin.

Open Regedit and Select File/ Import and try importing your .reg file that way.