It turns out that it's pretty straightforward joyful thing to do. The Analysis Services server, PowerPivot included, uses the SQL Server setup infrastructure, and so does its setup logging.
First off, you go where the logs are placed. You can find them at
[SystemDrive]\Program Files\Microsoft SQL Server\100\Setup Bootstrap\Log.
Look for a file called details.txt under the folders at \Log.
Once you found them, you can search for the text "ASSPI_Install". With that, you’ll go straight to the beginning of the PowerPivot setup logging.
When bad things happen during setup, this is the place where you should start looking for some answers.