I did not have enough rep to answer or comment on the original question, but I wanted to contribute my findings. See Can't install .net 3.5 on Windows 10 for the original question. I received a warning similar to the one below, although the error code might have been different.
The following feature couldn't be installed:
.NET Framework 3.5 (includes .NET 2.0 and 3.0)
Error code: 0x800F081F
I tried running the update through the "Windows Features" dialog after each change, and reverted a change when it did not work where applicable. I tried different VPN's, changing the settings for "Specify settings for optional component installation and component repair" (source: http://www.askvg.com/fix-cant-install-microsoft-net-framework-3-5-in-windows-8-and-later/), however I did not try offline installation using DISM.exe because I did not have a Win 10 image handy.
While in the process of getting the image, I tried the default Microsoft online troubleshooter, and to my surprise installation of .NET 3.5 succeeded after performing the following step:
Fix Windows file corruption:
DISM.exe /Online /Cleanup-image /Restorehealth
sfc /scannow
(see: https://support.microsoft.com/en-us/help/10164/fix-windows-update-errors).
Neither tool indicated that there was anything wrong, so perhaps I made a mistake in isolating my tests.
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