Thank you for letting me know. I think it really was for the best. Hopefully you will have no more trouble.
The honest answer is that I was out of ideas, and those links were my final hope. I specialise in fixing CheckSUR.logs, and I got that to the point where it detected no more errors. Once that didn't fix it, I took some of the other log types, such as CBS.log and WindowsUpdate.log, which I do not specialise in to such an extent, but still couldn't see anything which I could fix. Finally, I looked through my past notes and searched Google, and even that didn't find a solution. I was completely out of ideas.
Your only other solution was to try to find someone else who could fix this issue, but your chances were next to zero. There are 4 of us who almost exclusively deal with Windows Update issues. Those are Flavius, MowGreen, TaurAdrian, niemiro.
Unfortunately, I doubt that any of these people would have been able to fix your problem. TaurAdrian specialises in Windows Server Update Services (WSUS), the business side of Windows Update, and the networking side, mainly. Your issues doesn't really fit her (I think??) expertise. Then you had a choice between Flavius and MowGreen. Flavius is much more similar to me, and probably would have approached the fix in a very similar way to me. In this case, he probably would have taken your entire registry, patched it up on his computer to the best of his ability, and sent it back to you. It would have been a very long shot. He might have pulled it off, he might not have. But with such damage, he could only have got it similar to how it once was, not exactly right, and it may not have taken. Finally, MowGreen. He specialises in CBS.log and WindowsUpdate.log. However, he also has a phenomenal amount of experience. He quite likely has knowledge on both this particular IE9 error, and possibly some more titbits on updates which get repeatedly re-offered. However, I strongly suspect that you are not the standard and simple case, and that standard and simple fixes probably wouldn't completely fix your computer.
I suspect that any of the others would have had some new ideas, tried some new things, but I just have this niggling doubt that they wouldn't have been able to fix this machine, and the honest answer is that I don't know anybody who has a better chance than them.
I am sorry that it had to end like this, but I would like to say that it has been truly wonderful to work with you, and I wish you a healthy computer for the future!