This is one of the case where Windows Update went sour, very sour for me indeed because greatly affect me and my line-of-work.

Refer to this KB3005628, who (unlucky) installed KB2966827 or KB2966828 yet not enabled .NET3.5, you will be having difficulties in enabling the .NET3.5 features and thus impact lots of other functionality whereby SQL not able to proceed, some tools not able to run without .NET3.5.

Fix is simple, uninstalled the two botched update, KB2966827 & KB2966828. Restart your PC / Server and try to enable .NET3.5 feature again.

.NET3.5 Failed to install