I had this same problem installing SQL Server 2014. Turns out it was due to a Windows Phone toolkit that I had installed back in 2010. If you run into this, make sure you uninstall any Windows phone stuff that isn't current.
I figured it out by looking at the log, which can be found by clicking "Detailed Report," which opens an HTML file. The file path is conveniently displayed within the HTML page. Open the directory that the file is in and look for "Detail.txt." Then search for the word "fail."
In my case there was a line showing WP_[something] as "Installed." I searched for the WP_ item and came across some blog posts about trouble uninstalling Windows Phone toolkits.
When I attempted to uninstall the windows phone I ran into more trouble. The uninstaller wanted to install three packages instead of uninstalling the toolkit. Eventually found this blog post: http://blogs.msdn.com/b/astebner/archive/2010/07/12/10037442.aspx linking to this XNA cleanup tool: http://blogs.msdn.com/b/astebner/archive/2009/04/10/9544320.aspx.
I ran the cleanup tool and finally SQL Server installer passed the check and allowed me to install. Hope this helps someone.