Computer attempts the same update on every shutdown

OK, let's have a look at the new logs, then
upload the following files, and I'll take another look

C:\Windows\Logs\CBS\CBS.log
C:\Windows\windowsupdate.log
C:\Windows\setupact.log
C:\WIndows\Logs\DISM\dism.log
C:\Windows\SoftwareDistribution\ReportingEvents.log

Here's the critical errors that I can find....

Code:

{4F70F07B-691A-4FF0-8C48-5098917BC255} 2013-11-01 17:43:23:062+0900 1 188 102 {00000000-0000-0000-0000-000000000000} 0 0 AutomaticUpdates Success Content Install Installation Ready: The following updates are downloaded and ready for installation. This computer is currently scheduled to install these updates on ‎2013‎年‎11‎月‎2‎日 at 3:00:  - x64 ベース システム Windows 7 用 Internet Explorer 10
{F42ED737-7C60-4F17-829A-917DAEC5635F} 2013-11-01 17:46:35:756+0900 1 198 101 {5F84379F-7C14-472F-B560-62A0CDEC6F31} 204 80070643 AutomaticUpdates Failure Content Install Installation Failure: Windows failed to install the following update with error 0x80070643: x64 ベース システム Windows 7 用 Internet Explorer 10.

cbs.log

Code:

2013-11-01 17:43:19, Info                  CBS    Session: 30332638_1782867965 initialized by client WindowsUpdateAgent.
2013-11-01 17:43:19, Info                  CBS    Identity missing version. [HRESULT = 0x80070057 - E_INVALIDARG]
2013-11-01 17:43:19, Error                 CBS    Failed to shred identity: Microsoft-Windows-InternetExplorer-LanguagePack [HRESULT = 0x80070057 - E_INVALIDARG]

windowsupdate.log

Code:

 Line 13213: 2013-11-02 00:34:24:947 1064 404 Agent WARNING: Failed to evaluate Installed rule, updateId = {818701AF-1182-45C2-BD1E-17068AD171D6}.101, hr = 80242013
 Line 13409: 2013-11-02 00:54:25:997 1064 84c PT WARNING: Cached cookie has expired or new PID is available
 Line 13591: 2013-11-02 01:05:50:583 1064 84c Agent WARNING: Failed to evaluate Installed rule, updateId = {818701AF-1182-45C2-BD1E-17068AD171D6}.101, hr = 80242013
 Line 13660: 2013-11-02 01:10:39:699 1064 1440 Agent WARNING: WU client fails CClientCallRecorder::RemoveService with error 0x80248014
 Line 13661: 2013-11-02 01:10:39:699 3328 c18 COMAPI WARNING: ISusInternal::RemoveService failed, hr=80248014

The indications are that there is some problem with the necessary updates that IE10 attempts to download and install - at least for the attempt you made to install at shutdown on 1st.

I think you need to force an install using the external downloader.

Download Internet Explorer 10 - Microsoft Windows

pick the version that matches your system and run it - make sure that you are connected to the internet during the install.
What happens??

OK - post the new CBS.log and windowsupdate.log files.
Somewhere there is some residual system corruption - the trick is to get Windows to tell us where it is :)

Just a thought.
Noel could this out dated program cause this problem?
Could MSE help?
From Supercain Specs.

Antivirus Windows Defender

supercain please don't change things without Noil's guidance.

Defender isn't an anti virus :) - it's an anti malware app.
Cettainly, if it's not backed up by a proper AV then it could be a problem!