I also created a BAT file that runs the Windows Update full system reset as suggested by Microsoft. In fact, let me post that here for you.
Create a TXT file on your desktop. Name it WUFix.bat and make sure the file extension changes, not just Windows naming it WUFix.bat.txt. Then put the following inside it:
@echo off
net stop bits
net stop wuauserv
net stop appidsvc
net stop cryptsvc
del "%ALLUSERSPROFILE%\Application Data\Microsoft\Network\Downloader\qmgr*.dat"
ren %systemroot%\SoftwareDistribution SoftwareDistribution.bak
ren %systemroot%\system32\catroot2 catroot2.bak
sc.exe sdset bits D:(A;;CCLCSWRPWPDTLOCRRC;;;SY)(A;;CCDCLCSWRPWPDTLOCRSDRCWDWO;;;BA)(A;;CCLCSWLOCRRC;;;AU)(A;;CCLCSWRPWPDTLOCRRC;;;PU)
sc.exe sdset wuauserv D:(A;;CCLCSWRPWPDTLOCRRC;;;SY)(A;;CCDCLCSWRPWPDTLOCRSDRCWDWO;;;BA)(A;;CCLCSWLOCRRC;;;AU)(A;;CCLCSWRPWPDTLOCRRC;;;PU)
cd /d %windir%\system32
regsvr32.exe atl.dll
regsvr32.exe urlmon.dll
regsvr32.exe mshtml.dll
regsvr32.exe shdocvw.dll
regsvr32.exe browseui.dll
regsvr32.exe jscript.dll
regsvr32.exe vbscript.dll
regsvr32.exe scrrun.dll
regsvr32.exe msxml.dll
regsvr32.exe msxml3.dll
regsvr32.exe msxml6.dll
regsvr32.exe actxprxy.dll
regsvr32.exe softpub.dll
regsvr32.exe wintrust.dll
regsvr32.exe dssenh.dll
regsvr32.exe rsaenh.dll
regsvr32.exe gpkcsp.dll
regsvr32.exe sccbase.dll
regsvr32.exe slbcsp.dll
regsvr32.exe cryptdlg.dll
regsvr32.exe oleaut32.dll
regsvr32.exe ole32.dll
regsvr32.exe shell32.dll
regsvr32.exe initpki.dll
regsvr32.exe wuapi.dll
regsvr32.exe wuaueng.dll
regsvr32.exe wuaueng1.dll
regsvr32.exe wucltui.dll
regsvr32.exe wups.dll
regsvr32.exe wups2.dll
regsvr32.exe wuweb.dll
regsvr32.exe qmgr.dll
regsvr32.exe qmgrprxy.dll
regsvr32.exe wucltux.dll
regsvr32.exe muweb.dll
regsvr32.exe wuwebv.dll
netsh winsock reset
net start bits
net start wuauserv
net start appidsvc
net start cryptsvc
Then save all this to the file, then run as administrator. When it's done, restart the computer and see if Windows Update runs.
ALERT: Be aware, this BAT file will make some powerful changes to certain key Windows system directories, such as resetting not only Windows Update file stores but also resetting your Cryptography store folder and also re-registers all the DLL files used by Windows Update. This BAT file I use all the time on systems that have WU problems and it's never bricked a system yet, but USE AT YOUR OWN RISK. If the problem isn't with the Windows Update file store or a DLL issue, then this won't solve your problem.