I have set up numerous cases with this same issue and the resolution comes down to a repair install. There's no easy fix. I've set up cases with "real" engineers.
If you are looking for a quick fix, I'm not seeing one coming.
I was able to resolve this issue, but the solution required another computer. My clients laptop reported that it had completed the automatic IE10 upgrade but had not. I tried downloading the offline installation files for IE10 (to a jump drive using a healthy pc), but the failed pc said that a newer version of IE10 was already installed. I tried uninstalling, and it said that not all of the updates were removed successfully. There were no restore points available to roll back to. It was an endless loop!!! My solution was this:
I found another computer running the same service pack and edition of windows ( In my case Windows 7 Pro SP1 32 Bit ). I made sure that System restore was enabled on the good laptop. Created a restore point. Then manually updated that computer to IE10. After successful update, I copied the missing Dll files to a jump drive, and pasted them into the system32 directory of my failed computer. This FINALLY allowed me to remove IE 10 from my failed computer, and install the IE9 + IE10 Block.
Hopefully this helps someone else, I have used these forums enough that it feels good to return the favor