Latest Windows 10 update

That attachment shows that you now have 8 updates that require Restart, NOT reboot, to install. When doing Updates you are not supposed to click Shut Down, you need to click Restart.
 There is a big difference between shut down and restart.
In Windows 10 if you have Fast Boot enabled, and I believe it is by default so unless you have turned it off then it is on and then hitting Shut Down is not a full, complete shut down but is an abbreviated form of hibernation and uses a hibernation file which saves a file image of the OS state as well as the application program states so when the computer boots up it boots up fast. Updates usually cannot continue to install because these files start quickly BEFORE the update can complete because other files are interfering.

Restart intentionally saves absolutely nothing regarding the OS state or the applications states the computer is 100% turned off. After shutting down it reloads the OS from scratch from the disc drive files that make up the OS.

You MUST hit  Restart as it tells you on the Windows Update information, NOT Shut Down.

I guess this is what you mean? When I hit that button the computer shuts off and starts up right away again, exactly as if I had hit re-boot. 

I did that several times too with the same thing happening. I even shut down the computer and then started it up again hoping that would work but no it did not either.

I notice that you now only have the one update pending. In your reply #31 you had 8 updates waiting for restart and now in the latest attachment you just have the one update waiting for restart so you must be getting updates otherwise it would still show 8 of them

One final thought.
As your computer is not automatically restarting but requiring you to manually restart it could be worth checking the Restart options on the
WU page to allow restarts ar any time. It will not do so during ‘active hours’

A long shot perhaps ....

I checked the Restart options and as far as I can see it should be restarting automatically. 

This is very odd, when I click the link I do not get a number of fix steps, I get Two, well actually 3 and the 2nd one is the Windows Update Troubleshooter.
How very strange. I have tried this with four different browsers just in case...whatever??? and I get the same page each time.

The page says, "We’ll walk you through a series of troubleshooting steps to get your Windows up to date. Be sure to follow the steps in order."
1st step asks operating system.
2nd step is Windows Troubleshooting Tool.

You're asked if the problem is fixed and if you say no then you get a link for the 3rd step which is to Download the most recent Servicing Stack Update (SSU)
KB4090914

www.catalog.update.microsoft.com/Search.aspx?q=KB4090914

You download and install the one that is for your particular operating system. Once that is installed then it says to "Restart your device and check for updates."

Not sure what happens after that since I am not having trouble I didn't install that KB.

I was just reading through what you've done thus far and you said you cannot run Command Prompt (Administrator) because you don't recall your Administrator password. You don't need the password all you have to do is select to run it as Administrator.
Go to Start, Windows System,  Command Prompt and it will be shown to you, right click and choose Run as Administrator It will open and you can then follow the directions given.

Be sure to run BOTH the DISM and SFC commands, not just one of them.

I was able to use the prompt as Administrator and followed the two steps as shown. Then I restarted the computer and got the same results as in the picture before and a notification as always "We couldn't finish installing updates" I went back to the website and clicked on NO but the next few steps are too involved and I don't feel I am competent to do those. So that's it...I give up for now (again ;-)

Thanks for your kind words. Hope the next update will fix the problem. In any case I shall keep you all informed. 

I shall wait. Thanks

Correction on build number, this new KB will update Windows 10 to build number 16299.402 not 261...etc.

April 23, 2018—KB4093105 (OS Build 16299.402)

I shall wait until it is offered to me via Automatic Update.

I should expand my post above and mention that I don't normally do Windows Updates by downloading them and installing them. I let Windows Update do it when they come available through the normal update process which is the recommended way to update Windows. Tonight I was bored and knowing that Vera was waiting for the next Windows update I decided to download it, install it and see if I had any issues with the update. I didn't.

The main purpose of my original post was to let Vera know the update she was waiting for had arrived. This not the Spring Update which is still pending but should arrive real soon.