How to get rights to copy to Root of C:

That doesn't make sense, that's far too large to have been created by installing Windows. That size is consistent with an OEM factory reset recovery partition.

To the best of my memory, that is how the drive came when I bought this computer (Hewlett Packard Compact Pro, 6305 Small Form Factor)...used from a refurbisher/reseller, with Windows 10 Pro, preinstalled. I have had this computer a year, give or take...I do not remember anything about how the partitions were set-up on it when I got it...remember, I am 74 years old (my memory for details is fading).

How many recovery partitions does disk management say you have? That may not be the one that Windows is actually using as the active recovery partition.

One recovery partition. As the screenshot shows:

EDIT: your emachines ET1331G-03w was supplied with Windows 7 Ultimate 64-bit. That 16GB recovery partition will almost certainly contain the Windows 7 factory reset image. Windows 10 will likely be using another partition.

That was my previous computer about a year or so ago...see above for my current computer.

The plot thickens...on the current automatic attempt to install "important security upgrades on your pc", error code 0xc0000005 was generated.

I suggest you shrink the C: partition by at least 600MB, preferably 1GB. If (as it seems) this is an MBR partitioned drive, there can be up to four partitions, so there can be one more. Setup should able to create a new recovery partition in the unallocated space you'd create at the end of the drive.

"Setup should able to create a new recovery partition..." A statement. I do not understand what I am supposed to do.

As a precaution, it's always a good idea to make a system image of the existing drive before making changes like these.

"system image"? I have a clone of the drive...is that a "system image"?
Here is an expanded screenshot:

I suggest you shrink the C: partition by at least 600MB, preferably 1GB. If (as it seems) this is an MBR partitioned drive, there can be up to four partitions, so there can be one more. Setup should able to create a new recovery partition in the unallocated space you'd create at the end of the drive.

I can figure out how to shrink the C: partition by 1GB.

But have no idea how to proceed from there.

Shrunk C: drive by 1GB. The screenshot of the drive as shrunk, I will attempt the Windows 10 upgrade tonight and see how it goes. I should know if it works tomorrow A.M.

No joy. After download and reboot:
"Feature update to Windows 10 version 1709- Error 0xc1900200"

dahermit said:

No joy. After download and reboot:
"Feature update to Windows 10 version 1709- Error 0xc1900200"

Nothing has worked. Windows Update Assistant still tries to download the 1709 update which still ends in error 0xc1900200.
I have given up. The hell with it. Not worth the aggravation. I found a workaround on this forum where one can uninstall Windows Update Assistant, delete the folder: C:\Windows\UpdateAssistant, delete the tasks, Update Assistant and UpdateAssistantCalenderRun. According to the post where I found it, it keeps the Update Assistant from running and automatically trying to download the 1709 update.