Off the top of my head it could be a bad ignition switch, a bad fuse, a bad battery, a bad starter or in some vehicles the manufacturer has an immobilizer set where it will lock the car from starting in case of a theft attempt. Sometimes putting the wrong key in the ignition will activate the immobilizer. When this happens you will usually see a light in the console with a lock or a key icon. In some cars if you leave the key in the ignition and turn the key (but not crank it), and leave the key in for 30 minutes it will disable the immobilizer.

If this was my car I would do go about repairing the problem in this order:

• Make sure the car is in park. I have seen this before when people forget that the car is not in park and doesn't let the car start.
• Find out if the car has an immobilizer.
• If it does then try the immobilizer trick or find out how to disable it.
• Check fuses.
• Have battery tested for free at an auto parts store.
• Remove starter and have it tested for free at an auto parts store.
• Replace ignition switch.
• If problem persisted then I would take it to a reputable shop.