Yes. It would be a little trouble to do, though. What would I do with it in another computer?
My first thought is to run various virus scans because at least then you know a rootkit can't be circumventing the scanning capabilities, but in your shoes I would want to queue up a load of ideas rather than take a disk out, do one thing, put it back in again, rinse and repeat...
Another thought is to try browsing to the problematic folders from the other PC, but first I'd like to know what it says the permissions are (in the machine that disk is normally in). Out of curiosity I might be inclined to (temporarily) reset permissions to something like everyone:F just to see whether it makes any difference to your ability to access the folders. I would then try it in another machine to see whether there's any difference in accessing it.
Hopefully needless to say, but absolutely don't run any binaries from the disk in question while it's connected to the other machine.
Can you confirm whether my summary of the problems is correct?:
Historical point - User disappears from welcome screen, files were still present.
Creating another user allowed you (probably once you've confirmed a security alteration) to copy old user's files into new profile, you could access the files, but then it decided that you weren't allowed to access those files (possible coincidence being setting default player/browser).
Virus checks so far haven't turned up anything, checked with Malwarebytes too.
Question - In Malwarebytes, did you do a custom scan, told it to check for rootkits and to check the entire boot volume?
Full file system check turned up nothing of particular interest. Anything recent error/warning-wise in the system log (Windows Event Viewer)?
Other disk checks also didn't turn up anything.
Someone mentioned file extensions and malware presenting something as a text file when it's actually .txt.exe. Have you switched off hiding file extensions? To what end I'm not sure, perhaps you'll notice something awry when folder browsing.