So the red light just means it's charging (and not dead). Long press the power button until you get sign of life.
Try to call the device from another phone. If it rings, it's the screen.
If not, try long pressing power, volume up and home buttons. Hold them until the Samsung logo appears. Release the power button but not the other two! If you got that far, you may be able to reboot from there. If no luck with any button combination, take it to Samsung shop, it should still be under warranty..