Microsoft products cannot connect via https - windows

Question

We're having a problem here that a few hours on Google would suggest is very common but mostly unresolved.
Since upgrading to Windows 8.1, no Microsoft product can connect to any site via a secure channel, specifically TLS channels.
Internet Explorer 11 can connect to http web sites (e.g. msn), but will not connect to any https web sites (e.g. login.live.com, google). Attempting to connect to an https site results in 'This page cannot be displayed'. Other browsers, for example Firefox and Chrome, can connect to https web sites perfectly well.
On its own that wouldn't be an issue, we could just use Firefox (which is our default browser anyway), however every single Microsoft product uses the same settings and transports as Internet Explorer, and so none of those can connect to secure sites either.
This means that Windows Update won't work, and that we cannot register any Microsoft software (e.g. Office, Visual Studio, etc). Attempting to do so results in 'A communication error has occurred.'
Sometimes it gives an error code, for example attempting to activate Office gives 'A communication error has occured. Please verify that you have connectivity to the Internet and try again (0x80072F8F).
Googling that code suggests checking the BIOS date and time (we did, all correct) and resetting Internet settings (we did, to no avail).
We had the same problem crop up on Windows 7 after a Windows Update, which we fixed by going into Internet Options and disabling TLS 1.0 and re-registering some DLLs, however that hasn't fixed the issue here.
Other things we've tried are:-
Disabling SPDY/3
Disabling SSL 2.0
Every combination of enabled and disabled TLS 1.0, 1.1 and 1.2
Disabling Enhanced Protected Mode
Clearing SSL state
Uninstalling Internet Explorer 11
As I mentioned at the start, this only affects Microsoft products, anything from other companies or anything we write ourselves works perfectly, which would suggest there's some specific settings or code that Microsoft use that is the root of the issue.
Anyone else had this and managed to solve it?

Answer 1

I had this same problem with IE and this is what fixed it for me.
You should open a Command Prompt as Administrator and run the following commands:
regsvr32 Softpub.dll /s
regsvr32 Initpki.dll /s
regsvr32 Wintrust.dll /s
regsvr32 Mssip32.dll /s
Restart your computer and try accessing the HTTPS sites again with IE. These commands re-register the Dynamic-link library files which are called when you connect to an HTTPS site using Windows programs.
Here is the Windows support page which had this info:
https://support.microsoft.com/en-us/help/813444/you-cannot-log-in-to-or-connect-to-secured-web-sites-in-internet-explo
I had this same problem with trying to access domains in Powershell over HTTPS, but Google Chrome could access the HTTPS sites just fine on the same machine, so I knew it was a Windows-system issue and not a networking issue.
Hope this helps. Good luck!