After you made a full image, onto a target drive, of the source drive; as a test, you did restore that full image onto your normal OS and data drive, correct? Because the original computer restoration test worked flawlessly, you are assured that the full image can be restored onto a hard-drive of a new computer - should that day ever come.
"...All I really need is all of my user profiles and their data, mainly desktop folders. I was manually taking what I needed by navigating the C drive and specific user folders but I have way too many and it will take too long. I tried to copy and paste all of them but it will not allow me unless I first click each individual folder to request the required permissions. How can i copy and paste all of them to a new drive without the need for the special permissions?"
I realize it is 2AM over here, I still do not understand why all of the above is necessary. If the full image making and the full image restoring works, why is all that copying necessary? Even if you restored the full image on "top of" the Windows 10 computer, everything on the original hard-drive is now on the Windows 10 computer -- if the following boot of the target computer did not work, it probably:
-- had something to do with: target drives' partition(s) not being marked and set correctly by the restoration process
-- did not have something to do with alleged missing user profile material
I know a little bit about platter-driven internal HDs, platter-driven external HDs' backup, restore, cloning operations, therefore I must be missing something or some things about your two computers situation.
"Take care of thy backups and thy restores shall take care of thee." -- Ben Franklin revisited.
Backup, backup, backup! -- Lady Fitzgerald (w7forums)
Clone or Image often! Backup... -- RockE (WSL)
"I heard Spock finally got colander!" "I believe the word is Kolinahr." "Oh."