I am also a little confused about what we need to do.
If your problem is that you cannot install SP1, the chances are you are being restricted because of problems with earlier updates. Even if an update showed as failed initially and then later as successful, it may have still left your system in an unsyncronized state. This is the information I was trying to get from your WindowsUpdate.log, but you have not allowed access to the latest information.
There is also a CBS.log that could be checked if it is copied to the desktop. WindowsUpdate writes events to this log also.
If it hasn't been suggested already, I would ask you open Windows Update and look at the history. Make note of the updates that originally showed as "failed".
After that, go back to the main page and click on "Installed Updates" in the lower left of the window. Find those updates and right click and select "Uninstall".
Now let Windows Update find them again and see if they will install correctly the first time. A good internet connection is essential for a good install.
Also, are you showing a gold shield on your shutdown button on the Start Menu?
If nothing else works, go to the
Microsoft site and download the SP1 update directly. You will have to authenticate to download, which in itself might help your situation.