Step 1:
Warning: This script was written specifically for this user, for use on that particular machine. Do not run this script on another machine.
Download the attachment and extract it.
Open the extracted folder, double-click the file regfix.reg.
When prompted allow to change the registry settings.
Report the result.
Step 2:
Restart the machine.
Check Windows Update again and report the result.
If it fails attach the files C:\Windows\Logs\CBS\cbs.log and C:\Windows\INF\setupapi.dev.log to your next reply.