Folks, this issue has already been solved. Please read the thread, it is no longer necessary to post logs.
For those of you lacking the attention span to read:
This is an issue with the update. It is not your computer. The update tries to install a version of Windows Live ID Sign-in Assistant that is older than the one currently on your PC, so the install fails and rolls back. The update has been removed from Windows Update, and will presumably be corrected, and offered again.
If you do not wish to see the update, stop the Windows Update service using Administrative Tools--->Services, then delete the "C:\Windows\SoftwareDistribution" folder, and restart the service.
For you trolls who just cannot resist stating that you are too smug or cool to use Windows or the software, 2010 called, they want their lines back. Get a life.