Hi Jamie,
The 4th last line shows that the installation of Office KB941637 ended with an error code of 17031 - Invalid Baseline.
This error occurs when people are using a beta or non-standard version of Office 2007. The package is designed to install only on official Office 2007 RTM or SP1 releases. We have seen this type of error on corporate machines where the RC candidate of SP1 was pushed out to users instead of the official SP1.
If you have an Office SP1 beta, prerelease or release candidate, you should uninstall it and update to the official SP1 version and then apply this hotfix. You can run this hotfix separately and, if it succeeds, the Office Live Addin will detect and skip over this hotfix.
For reference, it appears that the hotfix was decompressed to your HD to the following folder: (other users should see a similar file referenced in the 5th last line in the log) 'C:\Users\jamie\AppData\Local\Temp\VSD27BD.tmp\OfficeKB941637'. You can run this hotfix directly once you get your Office version back to an official SP1 state.
As a heads up, users that install this package on Office 2007 RTM and THEN upgrade to Office SP1 will lose the benefit of the hotfix. We recommend upgrading to SP1 first and then applying this hotfix.