I don't remember, but if you have an OEM system, I have no experience with how it will behave. But if you have your own install of a retail version, you can start the install while running Windows 7 and start the install from there. Do not boot to the DVD.
Then do a custom install over you current version and it will redo the OS. It is called a Repair Install, and you can look it up on the net and make sure you know how it works. It is supposed to maintain your data and just replace the basic install.
If you do not feel comfortable, then please do not take such an action. Things can always go wrong...
The last attachment really doesn't tell me anything except you have some .Net 4 updates from May 5, 2013, so the basic client profile updates seem to be working.
Again, I just do not know what to tell you. I still feel you have having some type of connection problem with the Windows Update server site. If you want, attach the WindowUpdate.log again and I will see if anything has changed since you uninstalled the updates.
You might try download some updates manually and trying to install. I have not suggested this because I do not know where you stand on which ones you are missing. But if you do not have
KB2670838 you might try it since it was delivered for me on Feb 27. Use
IE and go to the Microsoft Catalog and download the update. It will want to install an activeX utility for the site to function.
Microsoft Update Catalog
If you already have that KB, the next one is KB2791765 and both are Updates for Windows.