Cannot turn on .Net 3.5 in Windows 8.1 Error Code: 0x800F0906

I was trying to install SQL Server Express 2014 on a Windows 8.1 box and got the error:

"Error while enabling Windows Feature: NetFx3, Error Code: -2146498298 ... "

Which basically means it failed to turn on .Net 3.5.

So I tried to do it manually via the Control Panel and was fronted with the error:

"Windows couldn't connecto to the internet to download the necessary files. Makes ure that you're connected to the internet and click 'Retry' to try again.

Error code: 0x800F0906"

Not a helpful message (as internet was connected) but a helpful error code.

After hours of googling around, I found two good resources:

1. This page explains a couple of options for fixing the error - none of which worked for me but has worked for others:

http://community.spiceworks.com/how_to/show/30581-install-net-3-5-on-windows-8

2. A Windows Update page which tells you to run the following update - which in turn removes two other updates from your computer:

https://support.microsoft.com/kb/3005628

Running this update didn't seem to remove updates 2966827 or 2966828 - so I removed them myself via the procedure:

1. Control panel > 'View installed updates' (on the left hand menu)
2. Search for KB2966827, select and uninstall
3. Search for KB2966828, select and uninstall

Once I did that, I was able to successfully turn on .Net 3.5 via the 'Turn Windows features on or off' dialog in the Control Panel > Programs and Features section.

And THEN I was able to install SQL Server Express *finally*...