How do I find the product key for Windows 8.1

That is not strictly correct. Windows will allow you to create a system image of your C: drive complete as it is at that time. The option can be found in the lower left corner of the File History setup page and this does not require 3rd party tools to create or use.

The Windows Recovery USB key can then boot your computer in the case of a complete O/S failure and this can detect the image if on an attached drive. It again requires no 3rd party tools.

Upgrading from Windows 8 to 8.1 does not generate a new key, you have a key. What that key will not let you do is install 8.1 direct. Microsoft have relented to some degree and allow you to download refresh media with that key but will still not allow a bare metal install.

In order for that to happen it would require a special setup image that would accept the 8.0 Product ID held within the key even though installing 8.1. Not impossible but a difficult precedent to start. Product ID filtering is a key component of the anti piracy measures being used.

As those specifically with the issue you describe are relatively few it is unlikely to change.

"That is not strictly correct. Windows will allow you to create a system image of your C: drive complete as it is at that time. The option can be found in the lower left corner of the File History setup page and this does not require 3rd party tools to create or use."

"As those specifically with the issue you describe are relatively few it is unlikely to change."

You speak the truth!  After looking here first:

I was searching the lower left corner to no avail and seeing as the main page "Back up Now" button says it only backs up copies of Documents, Music blah blah blah not the system itself i was undeterred and Windows Searched for File History when i found if i went to the Control Panel version of the File History;  it was indeed there:

Hallelujah! a "System Image Backup" link which allows you to put a Windows Backup Image on a Drive of your choice.

I just performed a backup and i hope it worked.  i created a file (80% less GB than the total of my C drive but i hope that is the compression used)  but there is now a set of files there under the "WindowsImageBackup" folder named after the C drive computer i back up.  

I like being incorrect and especially if its a Hairyfool setting me straight.  Let's just hope i don't have to use it.

Microsoft have certainly made access to this function obscure to say the least. You have also come across one of the annoying idiosyncrasies of Windows 8 in that the MUI has features lacking in Control Panel applet and vice versa.

Don't forget that the image by dint of where it is cannot be booted, you also need to create the USB recovery key as well. Just type "recovery" in the Start Menu. This special setup/diagnostics version has the ability to load the image for recovery as well as any restore points held on the O/S drive. One caveat is that driver support is limited and when I tested it I could not see the drive attached to USB3. Moving it to a USB 2 port resolved it.

That would be voila' (I see) Bonjour from France.

As those specifically with the issue you describe are relatively few it is unlikely to change.

Hairy F,  in your humble and esteemed opinion, what do you think is going to happen with Win 10?  Will they honor old Win 7, 8 and 8.1 Product Codes for the free upgrade and even downloadable installation ISOs?  or does the saga continue and we'll have to figure out all their idiosyncrasies out all over again?