You said you implemented the fix that I posted, if so, it should have resolved the issue, assuming after you got the error you ensured that Mathematica was not running when you implemented the fix. After doing the registry fix, do you still get the same error message in the screenshot in this post.
I've installed Mathematica several times on Windows 10 systems using the fix and they all worked without issues. You might want to ensure that when you uninstalled Mathematica all traces of it removed (ie. make sure the folders on the hard drive were removed and deleted, no registry keys are leftover for Mathematica.
Additionally, it shouldn't matter but you're version of Windows 10 is out of data, the latest version of v1607 (Anniversary Update) which puts the build number up to 10493. If all of the aforementioned still doesn't work, your only option is to contact Mathematica chat or phone support.
Good luck.