Did your computer ever have an older version of the IDE installed? 1.5.x versions left debris behind in C:/Users/(your username)/AppData/Arduino15 (note that appdata is a hidden folder). Delete the Arduino15 folder in that location if so.
Failing that, or if that doesn't apply to you
Open command window in the directory you installed Arduino to and type arduino_debug - it will run in debug mode and print an error that will (hopefully) point towards what the problem is.