Arduino Analog in over voltage
The input pin to the AVR processor on the board could very well be toast. The AVR itself may or may not be OK. 

The most likely reason that the computer shut down was that the 12V being applied to the AVR input caused a latchup on the microcontroller chip causing a massive current spike load on the USB supply line. That surge was seen back at the computer and as such it shut down due to the overload.

A much less likely scenario is that the +12V was fed back into the computer as an over voltage spike on the USB 5V line. The computer may have had an over voltage detector on that rail that caused the shut down or latchup occurred on some chip in the computer. 

I would re-test the AVR board when powered from a USB wall charger to see if it draws the normal amount of current or not. If normal proceed ahead. If massive then discard the AVR board.