Your install log file included the following:
Running helper with params: "C:\Program Files (x86)\Common Files\Autodesk Shared\AdskLicensing\10.1.0.3194\helper\AdskLicensingInstHelper.exe" upgrade isUpgraded
LicensingCustomAction.licIsSvcUpgraded [I] [17:14:08:625]: process exit code: 106
LicensingCustomAction.licIsSvcUpgraded [E] [17:14:08:626]: exit code: 0, output: Error: The specified service does not exist as an installed service.
This lines up with description that the install failed during licensing service installation. My initial suggestion would be to see if the following folder exists on your system: C:\Program Files (x86)\Common Files\Autodesk Shared\AdskLicensing. If so, run the uninstall.exe file located in this folder to remove the currently installed version of this component.
If that doesn't resolve the problem, then I recommend checking out this article, which covers how to download and install the latest version of the Autodesk licensing service.
Tony Michniewicz
Revit Software QA Analyst