You can try to register the following DLLs if Windows Update service is not starting up or having some issue updating/running Windows Updates:
1. Create a batch file and copy the following contents in it and then double click on it to register modules.
regsvr32 c:\windows\system32\vbscript.dll
regsvr32 c:\windows\system32\mshtml.dll
regsvr32 c:\windows\system32\msjava.dll
regsvr32 c:\windows\system32\jscript.dll
regsvr32 c:\windows\system32\msxml.dll
regsvr32 c:\windows\system32\actxprxy.dll
regsvr32 c:\windows\system32\shdocvw.dll
2. Restart the Windows Update and Automatic service
3. Stop the Cryptographic Service
4. Remove the folder \Windows\System32\Catroot2
5. Rename the \Windows\SoftwareDistribution folder.
This above folder is the restoration point for Windows Update service.
6. Now restart the Cryptographic Service.
7. Create another batch file and put the following lines in it and then double click on it to register the modules:
regsvr32 /s Softpub.dll
regsvr32 /s Mssip32.dll
regsvr32 /s Initpki.dll
regsvr32 softpub.dll
regsvr32 wintrust.dll
regsvr32 initpki.dll
regsvr32 dssenh.dll
regsvr32 rsaenh.dll
regsvr32 gpkcsp.dll
regsvr32 sccbase.dll
regsvr32 slbcsp.dll
regsvr32 cryptdlg.dll
regsvr32 Urlmon.dll
regsvr32 Shdocvw.dll
regsvr32 Msjava.dll
regsvr32 Actxprxy.dll
regsvr32 Oleaut32.dll
regsvr32 Mshtml.dll
regsvr32 msxml.dll
regsvr32 msxml2.dll
regsvr32 msxml3.dll
regsvr32 Browseui.dll
regsvr32 shell32.dll
regsvr32 wuapi.dll
regsvr32 wuaueng.dll
regsvr32 wuaueng1.dll
regsvr32 wucltui.dll
regsvr32 wups.dll
regsvr32 wuweb.dll
regsvr32 jscript.dll
regsvr32 atl.dll
regsvr32 Mssip32.dll
Your Windows Update should work.
