(1) I apologize for any unintended snarkiness, & I certainly didn't intend any. I can't even see any in that 2nd sentence. I do know, much earlier in this thread, I was going to say your computer was from Mars, not Japan - but I refrained!
(2) Restoring a system image backup is a cure only if the problem occurred after the backup was made. It returns all the partitions that are Windows back to the precise state they were in at the time of the backup. Obviously, it can't fix
a hardware failure or undo a BIOS or firmware update. Also I dimly recall a warning about credentials or something. If those are stored in Windows (& are difficult to reestablish), better make a new image if you know they have changed.
(3) I really don't know. But - if its important to have the region right - maybe it needs to be changed back to Japan. But maybe then it also will need to be brought back there too. It's just a suspicion, maybe a silly one. Were any of the other computers
moved that far?
(4) I think the real problem is that the computer is not linked at your Microsoft Account. Is that your only Microsoft Account? Even if you create a Microsoft Account on that computer (which links it), I think you still must open the Store & let it download
something. But the Store won't open for you. I don't know whether creating the account would be a fix for that.
If the Store would open, it would ask that you sign in, & that would establish the link (w/o having to create an account on the computer, I believe). So - I think the cure will be to get the Store to open. I already looked for that earlier & will look again.
Edit: Still have to look again for a Store fix, but...
(5) "It shows two of my computers that still exist and one that died a year ago. It doesn't show the one that has problems, though my digital licence is intact."
I'm not sure, but... If the computer itself has no Microsoft Account on it, then you might not see it until you get to the "Microsoft Store device management" page. Looks like you get directly there with this link...
account.microsoft.com/devices/content
Microsoft Store Device Management
(6) "As my previous message said, when adding a computer to Microsoft's database of my devices, Microsoft often forgets about computers that were added earlier."
All I can think of is, are you sure you sign them in to the same Microsoft Account? Sounds spooky.