Try putting it in Download Mode, Vol Down + Home + Power Button. The screen should go Blue-Green background or, rarely Black with text.
Read the screen and see which key is to restart (typically vol down) and see if that works.
Otherwise you phone may have an internal issue and need to see the current flow and find the culprit.
IF your phone has gotten wet, then there is a chance that the water inside created an issue.
good luck