Win 7 Home Prem X64 Update:KB2676521,KB2813170,80004002

I'm convinced that this is a registry problem - and that it's missing an entry somewhere.
The problem is working out where this entry may be, and it may be something as simple as a single bitflip in a datapoint. Such things can be incredibly difficult to discover.

Perhaps a look at the COMPONENTS hive would help?
Perhaps flushing the SoftwareDistribution folder?

The latter would be quickest - and may give instant results....


Open an Elevated Command Prompt
Run the following commands

NET STOP WUAUSERV
REN C:\WINDOWS\SoftwareDistribution SDOLD
NET START WUAUSERV

wait 15 minutes, and reboot
then wait 10 minutes, and open Windows Updates, and run a Check for Updates.

Install only the oldest update found - and reboot once installed.

Then post the new windowsupdate.log file before attempting to install any more updates.

This appears to be the critical error....

Code:

2013-08-05 10:20:21:609  432 142c Setup Evaluating applicability of setup package "WUClient-SelfUpdate-ActiveX~31bf3856ad364e35~amd64~~7.6.7600.256"
2013-08-05 10:20:22:763  432 142c Setup WARNING: Cbs StartSession, error = 0x80004002
2013-08-05 10:20:22:763  432 142c Setup FATAL: Applicability evaluation for setup package "WUClient-SelfUpdate-ActiveX~31bf3856ad364e35~amd64~~7.6.7600.256" failed, error = 0x80004002
2013-08-05 10:20:22:763  432 142c Setup FATAL: SelfUpdate check failed, err = 0x80004002
2013-08-05 10:20:22:763  432 142c Agent   * WARNING: Skipping scan, self-update check returned 0x80004002
2013-08-05 10:20:22:763  432 142c Agent   * WARNING: Exit code = 0x80004002

I'll do some research and get back to you.

Please run the following commands, and post the results....

REG LOAD HKLM\COMPONENTSC:\Windows\System32\config\COMPONENTS
REG QUERY "HKLM\SOFTWARE\Microsoft\Windows\CurrentVersion\Component Based Servicing\ApplicabilityEvaluationCache\WUClient-SelfUpdate-ActiveX~31bf3856ad364e35~amd64~~7.6.7600.256"
REG QUERY "HKLM\SOFTWARE\Microsoft\Windows\CurrentVersion\Component Based Servicing\Packages\WUClient-SelfUpdate-ActiveX~31bf3856ad364e35~amd64~~7.6.7600.256"
REG QUERY "HKLM\COMPONENTS\CanonicalData\Deployments\microsoft-w...deployment_31bf3856ad364e35_7.6.7600.256_3bdec3b2c6cadd60"
REG UNLOAD HKLM\COMPONENTS

Hmmm - back to the drawing-board - those are exactly the same results as I got

Lemme think about it for a while - Shout if you haven't heard in 24 hours!

Ah - I see what the problem was - I lost a space!

REG LOAD HKLM\COMPONENTS C:\Windows\System32\config\COMPONENTS
REG QUERY "HKLM\SOFTWARE\Microsoft\Windows\CurrentVersion\Component Based Servicing\ApplicabilityEvaluationCache\WUClient-SelfUpdate-ActiveX~31bf3856ad364e35~amd64~~7.6.7600.256"
REG QUERY "HKLM\SOFTWARE\Microsoft\Windows\CurrentVersion\Component Based Servicing\Packages\WUClient-SelfUpdate-ActiveX~31bf3856ad364e35~amd64~~7.6.7600.256"
REG QUERY "HKLM\COMPONENTS\CanonicalData\Deployments\microsoft-w...deployment_31bf3856ad364e35_7.6.7600.256_3bdec3b2c6cadd60"
REG UNLOAD HKLM\COMPONENTS

That should work! :)