All Windows 10 updates fail with Error 0x80070bc9

I upgraded to Windows 10 from Windows 7 seamlessly.

Everything works works perfectly that I can see, no crashes at all even when gaming, all completely stable.

Except I cannot install any windows updates whatsoever. I can download them, but not install them:

There were problems installing some updates, but we'll try again later. If you keep seeing this and want to search the web or contact support for information, this may help:

Cumulative Update for Windows 10 Version 1511 for x64-based Systems (KB3140743) - Error 0x80070bc9

Security Update for Adobe Flash Player for Windows 10 Version 1511 for x64-based Systems (KB3135782) - Error 0x80070bc9

Update for Windows 10 Version 1511 for x64-based Systems (KB3139907) - Error 0x80070bc9

That's the message I get when updating through 10's Update & Security program.

Something else that's a bit odd is a discrepancy between viewing my update history in windows 10's settings program and the control panel. Settings reports this:

Update history

No updates have been installed yet

Whereas if I visit control panel > programs and features > installed updates I see two entries under Microsoft Windows:

Update for Microsoft Windows (KB3133431)

Security Update for Microsoft Windows (KB3124263)

Attempting to uninstall either of these causes the following error:

Windows Update

An error has occurred. Not all of the updates were successfully uninstalled.

When I shutdown windows rather than shutting down it says:

Preparing your computer for update

Then shutsdown, then restarts, then says:

Installing update 35%

And then enters windows, but it hasn't installed the update. It just gets to 35% and then rollsback what it's done, I suppose.

This happens every time I start windows. Very annoying. Inorder to boot windows without this restart every time, I've deleted the downloaded (but not installed) update files from

C:\Windows\SoftwareDistribution\Download

And disabled the windows update service. However, I do want to be able to install updates for security reasons, if nothing else.

To fix any corruption that may have been causing this I've done the following.

As administrator, I've run the following commands:

> DISM /Online /Cleanup-Image /RestoreHealth

The restore operation completed successfully.
The operation completed successfully.

> chkdsk /r
and then answered Y to run chkdsk on reboot.

I rebooted and I let it run to 100% no problem. No messages given.

> sfc /scannow

Now here's a weird one, it was able to run a few days ago and reports that it successfully fixed corruption. However, now it returns:

There is a system repair pending which requires reboot to complete.  Restart

Windows and run sfc again.

It says this even after a clean boot (clean boot achieved by the method I stated above, deleting the update files), so I'm a bit confused why I get this message.

So what can I do to enable updates?

Reinstalling windows 10 should fix this. However, all my applications are installed really nicely, and I really like this installation, they way it's all organized ect. I do have two drives C: (boot drive), and an A: drive. Literally all of my applications are installed on A:, and all of the files I've created are also on A:.

So is there a pretty safe way to do a fresh install on C:, not touch A: and have all my programs still work? Maybe though backing up the registry across the reinstall? Or could my registry be causing the update problem?

However, I would really, really, really like it if someone just told be to delete some files, run a command and windows updates work again, as windows seems to be running flawlessly apart from this simple thing!

An answer like this: Windows updates fails with error 80070bc9

But for windows 10. Heck, it's possible that answer would work in 7 and 10 but I'd like some expert's advise.

Here is my update log: https://gist.github.com/anonymous/e690c56228c15febfd25

Download the logs found at C:/Windows/Logs here: https://www.dropbox.com/sh/g35n1jopvje3orz/AABUBKwBk4h8Cqqv-bdyDt09a?dl=0