Arduino Uno R3 board not working

Hi

I've been experimenting with various power supplies since I have an Arduino Motorshield Rev3. However, I think I did something wrong because I tried to hook up a 12V(3A) DC power supply to the Arduino Uno board itself which at first didn't seem to do anything. The green light on the board didn't light up and I then connected the normal USB cable to the Arduino Uno with the 12V dc supply connected to the motorshield instead. I also cut off the pin on the backside of the motorshield so it doesn't draw power from the Vin pin on the Arduino Uno. All seemed to be in order until I hooked up the Vin wire from my motorshield to my thumb joystick and then my computer suddenly shut down completely and now my Arduino Uno board is not woking. The LED for pin 13 is very dim and not blinking like before. Can the thumb joystick handle 12V(3A) or not?

Did I damage my Arduino Uno board? I know that the motorshield is designed to handle 12V at a max of 4A in total or 2A per channel. So I hope that it is not damaged as well...

Please advice.

Ian