There's always a log. Even on failed installs.
To get access to the temp files, open windows explorer and type %temp% in the address box and hit enter. This will take you to the temp directory. Sort the files by "Date Modifed" and you should see the log files.
Thanks Darin. I have been debating making an article describing these steps as well, since it is generally a common occurrence here.
Although we don't have the log files, it appears the issue is related to user directories being mapped to different locations. To check this, navigate within the registry to the following key:
If any of these paths are pointing to a different location other than the defaults begining with %USERPROFILE% then that would explain the issue. Change the modified path to the defaults which you can find attached:
Log out and log in with the Administrative account and try the installation again.