SQL Server 2014 installation fails: An error occurred for a dependency of the feature causing the setup process for the feature to fail

Solved my own problem with some more searching. The short version of the solution is that I needed to uninstall the SQL Server 2012 Native Client before doing this installation. (Not sure how that got installed on my machine; best guess is some Windows update.)

The resources that led me to the solution were:

https://social.msdn.microsoft.com/Forums/en-US/889167a7-1e51-4911-87fd-f1ed183fb839/failed-installation-of-sql-server-2014?forum=sqlsetupandupgrade - which led me to the details.txt file telling me exactly what failed.

https://connect.microsoft.com/SQLServer/feedback/details/769695/install-fail-sql-server-2012-developer-edition-an-error-occurred-for-a-dependency-of-the-feature

https://dba.stackexchange.com/questions/24563/not-able-to-install-any-piece-of-sql-server-2012-dev-edition-on-my-windows-7/25832#25832

Well, this is going to sound a little crazy, but if you are installing from a mounted ISO, extracting the ISO out to disk, as recommended on this Error Installing SQL Server 2012 Management Tools MSDN thread, cleared up the error for me. I used 7-Zip to extract it (the thread suggests that it won't work if you use WinZIP to extract it).