Help needed : Arduino Mega 2560 doesn't respond

Hi , I am using adafruit motor shield version 1.0 with arduino mega 2560 . After a while when I connected external 12V 2A power supply through power jack of arduino mega2560 board , the board got extremely hot and stopped to work and in this time another 12V battery was connected with motor shield as external power source . After that arduino mega2560 doesn't respond and not recognized by computer either ( not even the existence of any usb device , when I connect with pc I found nothing ) .

I have checked the on board voltage regulator , it works fine . while I connect arduino mega2560 with usb cable to my pc , the power LED lit up , but arduino mega2560 doesn't respond . The chip ( ATmega 2560 ) getting hotter slowly . What can I do to troubleshoot ? Please give me any Idea.

Seems like you fried the board.. You shouldn't draw more than 400mA total from the board.

If the processor chip is getting hot and the 5V supply is okay, that's usually a pretty good sign that a pin, or several, has been damaged, and its only a matter of time unti the whole chip fails.