Hi there I too had a very stubborn Windows Update problem (error 0x80070003 / Win 8.1 Home), and was finally able to fix it.
First, all the standard methods to fix WU failed (troubleshooter, manual reset of WU components, manual install of updates, sfc /scannow, DISM tool, etc.)
In particular, sfc and DISM never reported any errors. However, using the DISM tool led me to scrutinize the CBS.log file. When I did so, I noticed the following line:
CBS Failed to create file: \?\C:\windows\Servicing\Sessions\30435499_3442754378.xml [HRESULT = 0x80070003 - ERROR_PATH_NOT_FOUND]
This led me to look in the C:\Windows\Servicing directory, and I noticed that the Sessions folder did not exist. Or more accurately, there was a *file* called Sessions - apparently a corrupted version of the folder (dated about the time when updates stopped
working). I compared this to a working installation of Windows on another laptop, and saw that the folder did exist, and contained many xml files.
After playing around with the permissions I recreated the Sessions folder, tried again to (manually) install updates - and - it worked! So far I have been able to install upates, both manually and using the Control Panel.
The moral is, I think, take a close look at the CBS.log file and follow any leads it gives.
It's beyond me how the sfc and the DISM tool could fail to detect this problem. I'm guessing they both saw the "Sessions" file, and figured all was well.
Not sure if my situation applies to anyone else, but just in case, here it is.