As you have already reinstalled Windows, so this issue seems to be related to hardware.
I would again suggest you to contact a local tech shop for further assistance.
On August 16-17, Windows Update automatically initiated and eventually completed what appears to be 24 updates. I was able to cause a couple of manual updates after the automatic update was initiated to correct failed installs.
Since then, Windows Update does not show that it has checked for updates, and manual updates give the same old error message (80240442). So I ran the windows update troubleshooter. It gave the following report:
Issues found
Some security settings are missing or have been changed Fixed
Reset security settings Not run
Service registration is missing or corrupt Fixed
Reset service registration Completed
Windows Update error 0x80070057(2014-08-28-T-11_11_30A) Fixed
Resetting Windows Update data store Completed
Problems installing recent updates Fixed
Repair Windows Update Completed
Potential issues that were checked
Windows Update environment variables are incorrect Issue not present
Check for missing or corrupt files Issue not present
Windows Update services are not running Issue not present
Cryptographic service components are not registered Issue not present
InformationalDataStoreAndWULogFiles.zip
21.23MB
File Name: DataStoreAndWULogFiles.zip
Detection details Expand
InformationalError Report
RootCause: RC_DataStore
ErrorCode: 0x80070057
TimeDetected: 2014-08-28-T-11:11:30A
InformationalCollected File
File Name: CheckSURLog.cab
InformationalService Status
Problem with BITS service : The requested service has already been started. More help is available by typing NET HELPMSG 2182.
Collection information
Computer Name: JW-ASUS
Windows Version: 6.3
Architecture: x64
Time: Thursday, August 28, 2014 11:11:03 AM
Publisher details Expand
Background Intelligent Transfer Service
Find and fix problems that may prevent background downloads from working
Package Version: 1.2.1.20140627
Publisher: Microsoft Corporation
I then checked for updates, but got the error message. Also it now reads that I have "Never" checked for or installed updates (which isn't what it said a few minutes ago).
I then ran the troubleshooter a second time. This time there were only two problems reported, the Windows update error, this time coded as 0x80070057(2014-08-28-T-11_22_12A), and the Problems installing recent updates error. Both reported as "fixed."
I then checked for updates a third time. Still no success. Troubleshooter "fixed" same two problems again, plus the "service registration is missing or corrupt" error. Fourth update check, no success.
Given that Microsoft Update worked for a couple of days, this seems to suggest that the problem is with Windows Update, not my hardware. I am reluctant to pay a tech shop to tell me that Windows Update has a problem and that it can't be fixed.