Did anything unusual happen prior to this? For example, did you let the battery drain to zero? Did the phone suddenly stop working in the middle of usage despite plenty of battery left? Any water exposure?
Try this first: press and hold Power and Vol Down for about 30 seconds. Then wait a few seconds, and then press and hold Power for another 30 seconds. Still nothing?
Also, how long did you charge for? Make sure you charge using a plug and cable that you know are good, and let it charge undisturbed for at least 6 hours. Then try the above steps again.