I wish to thank you for this thread, it in part has helped me recover my Windows Update program as well. A couple changes to your instructions have occurred since you posted it and I wanted to share them in gratitude for this thread.
1. The KB3161608 Update has been superseded by KB3172605 and they provide a link to it on your KB3161608 update page which is: https://support.microsoft.com/en-us/kb/3172605
I down loaded the appropriate version for my operating system and it wouldn't install, it just hung while looking for update files on my computer.
2. So I followed their link at the bottom of the page labeled Troubleshoot problems with installing updates to https://support.microsoft.com/en-us/...#1TC=windows-7 and opened the What can I do if I'm having trouble installing updates and clicked on the Windows Update Troubleshooter text. That downloaded the software that analyzed my computer and fixed some registery entries and pointers.
3. Then I restarted my machine and clicked on the KB3172605 update I downloaded in step 1 which installed this time and rebooted again and it allowed me to run Windows Update successfully now!
I should note that I had to run step 3 without trying Windows Update after step 2 (which I tried once) because it caused the registry entries and pointers to be corrupted again. So I had to repeat step 2 and then 3 to clean it up for good.
Thanks again for this thread!