There are a few things that can cause this. While not all can be troubleshooted at home, I hope this information will be helpful to you and yield a possible solution.
1) Bad key - Try another one
2) Bad brake light switch - Make sure your brake lights work. If not, the switch is above the brake pedal.
3) Shifter not fully in park - Try moving it around a bit, try starting in both park and neutral
4) Bad immobilizer (aka EWS) - Nothing can be done - zero. Dealer equipment is required to fix. When this goes bad or out of alignment, the car does not get the proper signal that the correct key is present, and therefore, the car will not start and the starter will not be allowed to engage.
5) Bad transmission position switch (located on side of the auto transmission, accessed from under car) - This is what signals the car that it is in neutral/park and is safe to start.
6) Dead starter solenoid - Not likely, you would probably get some noise from it if this were the case.
7) Bad ignition switch/cylinder - Also unlikely as you would generally not get all other functions / power to come on inside the car in that case
I hope that is helpful, please let me know if you have further questions, or if I can clarify anything for you.
It has been my pleasure to help today and I wish you the best of luck with the vehicle.