won't start after i drive for a little bit on 2004 Ford Taurus

My car has recentely been not starting since the warmer weather has came. When I try to restart the car, everything inside the car will work, (radio, windows, air, lights, etc) but absolutely nothing happens when I turn the key. The battery and alternator are brand new, so I don't believe that is the problem. Can anyone please help me on this???

Asked by for the 2004 Ford Taurus
Make certain that your vehicle is securely in park.

It's hard to say, but it's possible the transmission range sensor may be intermittently failing. If so, the car may never recognize that you are in "Park". And if you are not seen as in park...the engine will not crank.