(1) I found this site...
http://gateway-us.custhelp.com/app/answers/list/
Gateway Support -- Top Answers
I entered "NE56R" into the "Select a product..." requestor (it's a button), & it pared down to 32 pages. Maybe try entering your serial number or SNID for even a greater pare
down. But read through those articles for basic information, sounds like normal information. Then I typed "push button reset" into the search box, & it pared down to 7 pages.
I certainly haven't read all the articles, but I still don't know what button it's referring to. Maybe look deeper than I did -- but certainly don't ever press that button! But read through the articles for sure.
At the "Support, Drivers & downloads" page, I see at best Win 8.1 drivers. But many of the articles do mention Win 10.
(2) "So sounds like every update puts it somewhere else."
It looks odd, all right. But it seems to have settled on putting them into partition 6 now.
(3) "Comment: You had mentioned shift + restart previously. I tested that this morning, computer ignored it, just booted as normal."
Normally, that happens when there is no Recovery partition that holds a WinRE.wim file &/or ReagentC doesn't point to it. An alternative to get there is...
"START, Settings, Update & Security, Recovery, Restart Now (under Advanced Startup)"
But I guess that won't work, either. But how have you been getting there? That's the "Choose an Option" screen, BTW.
(4) "The thing I might like to do is switch out the Win 8 on the working volume for a 10 image."
Well, there is a way to put a clean install of Windows capability into that partition. It might be easy or hard to do, I'd have to find & read it again. But why? You have your 2004 Windows Installation USB drive to do clean install's with. Wouldn't it be
better to put current system images into there instead?
(5) "Might try to do an Acronis backup image starting in the morning"
I don't know what's going on with your Acronis. I have Seagate's DiscWizard (which is an older version of Acronis True Image) -- & it makes images twice or more as quick as Windows system image backup & restore does. And the latter does it in under 20/so
minutes.
(6) "Hmm. Maybe I can assign a letter to each, the R again, and then use the chkdsk command"
Yep, but if you do it in Windows, likely you won't be able to repair partition 6 because Windows considers it in use maybe. Anyway, it won't repair mine. But /Scan is fine...
DiskPart
Select Disk 0
Select Part 2
Assign Letter=X <<< Put letter X on the Win 8 Recovery partition
Select Part 5
Assign Letter=Y <<< Put Y on partition 5
Select Part 6
Assign Letter=Z <<< Put Z on partition 6
Exit
CHKDSK X: /R <<< Does a repair
CHKDSK Y: /R <<< Does a repair
CHKDSK Z: /Scan <<< Does a scan only & reports errors
DiskPart
Select Disk 0
Select Part 2
Remove Letter=X <<< Remove the letter X
Select Part 5
Remove Letter=Y <<< Remove the letter Y
Select Part 6
Remove Letter=Z <<< Remove the letter Z
Exit