Arduino Due ( Atmel Microcontroller) IC Heat up and led goes off
Motor driver boards exist to allow an MCU to control a motor without having to supply its power. If you try to power motors from the Arduino as well, they draw too much current and things get hot or damaged.

The 3.3v pin is only for supplying modest amounts of current at 3.3v from a 5v Arduino. You can not back-power the board with it. I don't know what happens if you try, but I bet it isn't good...