From http://community.wolfram.com/groups/-/m/t/182178  :

My Tech Support reflex is to suggest resetting initialization files by holding down the SHIFT
and OPTION keys as Mathematica launches. (See http://support.wolfram.com/kb/3274.)

An alternative is to delete the folder Library/Mathematica/FrontEnd/ under your Home
directory, but that is by default hidden.


A diagnostic test is to try running the Mathematica Kernel by itself.  In a Finder window:
     go to the /Applications directory,
     Control-click (or right-click) on the Mathematica  app,
     choose "Show Package Contents" in the pop-up menu,
     in the next window open the Contents folder, then the MacOS folder.
     Double-click the MathKernel icon and a standalone kernel window will open.
This may show an error message explaining the problem, or it may run fine.
Either result is useful information.

In rare circumstances, once activation is complete the Front End opens without
problems when it stumbled before.

The Technical Support group (support@wolfram.com or support@wolfram.co.uk)
is the most direct place to go with cannot-run problems. Please include your
License Number or Activation Key.