The Program EasyVR Commander has a drop down box where you need to select the com port. Make sure the correct port is selected.
It looks like the EasyVR shield includes some jumpers. Have you set these for the Leonardo? A picture of your setup might help us find a problem.
It’s possible to communicate with EasyVR without an Arduino if you have a serial to USB adapter. Do you have a serial to USB adapter to use as an alternative to the Arduino?
Do you have any other Arduino boards?