Setup exit code: 0x00009C59 installing IE10 and Empty Win Feature List

WHY are you fiddling about with it? it's designed to 'just run'!
Please forget anything you see on that page (it's just some idiot showing off)

Just download it and follow the instructions in the Windows Update Posting Instructions and post the log file.

That's all you need to do - run the .msu each time.
It never actually installs anything, but it does use the TrustedInstaller service a lot, and corrects problems.

That log's more like it - and we can have some confidence in it now.

Code:

Unavailable repair files:
 winsxs\manifests\wow64_microsoft-windows-i..etexplorer-optional_31bf3856ad364e35_9.4.8112.20565_none_180ba330ce04c164.manifest
 servicing\packages\Win8IP-Microsoft-Windows-DownlevelApisets-Windows-WinIP-Package~31bf3856ad364e35~amd64~et-EE~7.1.7601.16492.mum
 servicing\packages\Win8IP-Microsoft-Windows-DownlevelApisets-Windows-WinIP-Package~31bf3856ad364e35~amd64~et-EE~7.1.7601.16492.mum
 servicing\packages\Win8IP-Microsoft-Windows-DownlevelApisets-Windows-WinIP-Package~31bf3856ad364e35~amd64~hi-IN~7.1.7601.16492.mum
 servicing\packages\Win8IP-Microsoft-Windows-DownlevelApisets-Windows-WinIP-Package~31bf3856ad364e35~amd64~hi-IN~7.1.7601.16492.mum
 servicing\packages\Win8IP-Microsoft-Windows-DownlevelApisets-Windows-WinIP-Package~31bf3856ad364e35~amd64~et-EE~7.1.7601.16492.cat
 servicing\packages\Win8IP-Microsoft-Windows-DownlevelApisets-Windows-WinIP-Package~31bf3856ad364e35~amd64~et-EE~7.1.7601.16492.cat
 servicing\packages\Win8IP-Microsoft-Windows-DownlevelApisets-Windows-WinIP-Package~31bf3856ad364e35~amd64~hi-IN~7.1.7601.16492.cat
 servicing\packages\Win8IP-Microsoft-Windows-DownlevelApisets-Windows-WinIP-Package~31bf3856ad364e35~amd64~hi-IN~7.1.7601.16492.cat

I'll post the new fix protocol in a few minutes.

I've uploaded a file - tmnab.zip - to my SkyDrive at Noel's SkyDrive
Please download and save it.
Right-click on the downloaded file, and select Extract all…
Extract to the default location - which will create a new folder tmnab in the same place.
Open this folder - there should be two folders inside it (Manifests, and Packages)

Copy the content of the Packages folder to the folder
C:\Windows\Temp\CheckSur\Servicing\Packages

And the content of the manifests folder (.manifest files) into this folder:

C:\Windows\Temp\CheckSur\Winsxs\Manifests

Now run the CheckSUR tool again (it may take a while)

Post the new CheckSUR.log file, and the CheckSUR.persist.log file.

I have most of the updates for Windows downloaded and extracted for just this purpose :) (It uses rather a lot of disk space, what with 4 versions, and various languages included!)

Your system is nowhere near as bad as some I've seen - the CheckSUR log is clean now - as to the cause, it could be any of a number of things including forcibly shutting the machine down during updates.

Please run another SFC /SCANNOW and post the new log, so we can check that the rest of the file system isn't affected by the changes we've achieved.

The SFC scan appears to have corrected the only remaining error :)

Time to try Windows Update again - do a manual scan first, and see what happens.