Steps to reproduce the issue

1. Prepare a web server to issue Content-Security-Headers that do not allow "unsafe-eval", e.g., with Apache, add header set Content-Security-Policy "default-src 'self' 'unsafe-inline'" to the VirtualHost configuration
2. Download and unpack Joomla to the web server
3. Visit your Joomla web server and follow the first-run installation tasks

Expected result

Installation starts once all conditions of the "Pre-Installation Checks" are met.
If there still is a problem, a helpful message should be displayed

Actual result

A popup "Process in progress. Please wait ..." comes up. Nothing else happens

System information (as much as possible)

Should not matter; tested with Ubuntu 12.04, Apache, Joomla 3.5.1

Additional comments

An additional Pre-Installation Check for good-enough Content-Security-Policy should be added.
It might simply be an additional line in the Pre-Installation Check table that shows a red "NO", which is changed into a green "YES" by some Javascript that relies on unsafe-inline and unsafe-eval to be present.
See also http://joomla.stackexchange.com/questions/16635/joomla-install-does-not-start