Windows Update and Defender have been disabled by malware (Windows 7 x64)

I get the following error when I try to run windows update and the windows update service does not appear in the list of services.

Windows Update cannot currently check for updates, because the service is not running. You may need to restart your computer.

I have downloaded and run a full scan with malware bytes in safe mode but that hasn't fixed the issue.

I also downloaded the windows update stand-alone installer (Windows6.1-KB947821-v22-x64.msu) and got the following error when I tried to run it:

Installer encountered an error: 0x80070424
The specified service does not exist as an installed service.

I am also missing the wuausrv registry key.

Under HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\services I have the following:
...
WSearchIfxPi
WudfPf
WUDFRd
...

An automatic FixIt for Windows update is available on Microsoft's Knowledge Base: http://support.microsoft.com/kb/971058

Personally I'd scan any such compromised system with the Avira boot CD: http://www.avira.com/en/download/product/avira-antivir-rescue-system

Also consider rebuilding (reinstalling everything). Since you can't really be sure to have removed every problem.