How to kill an Arduino when (dis)connecting 12V to Vin?
This answer has three parts:


What you described doing, and how that relates to elements of the Arduino design.
What you might have done, to cause the symptoms you describe
How you might start to narrow down the fault


What you described doing


  I had connected a 12V battery pack to VIN and GND.


That is not a problem, that is the input to the inboard regulator so it's fine




  I read that there's a diode on the board which selects the highest voltage in.


Yes, there is a Schottly MBR0520 diode between the USB supply and regulator output, the diode has a Vf of about 0.3v




  At one point I disconnected the pack and then reconnected..
  Point is, now the board wont start..


I'm not sure what to make of that, I don't see a reason for the board to get damaged

Arduino Nano schematic

What you might have inadvertently done

There's a list of ways to kill an Arduino which consists of


Method #1: Shorting I/O Pins to Ground
Method #2: Shorting I/O Pins to Each Other
Method #3: Apply Overvoltage to I/O Pins
Method #4: Apply External Vin Power Backwards
Method #5: Apply >5V to the 5V Connector Pin
Method #6: Apply >3.3V to the 3.3V Connector Pin
Method #7: Short Vin to GND
Method #8: Apply 5V External Power with Vin Load
Method #9: Apply >13V to Reset Pin
Method #10: Exceed Total Microcontroller Current


Number 4 and 7 are interesting candidates because, on the Nano, Vin and GND are adjacent.

If you have a Nano in a solderless breadboard, with wires connecting various IO pins to the breadboard, there is always the possibility of briefly accidentally touching a 12V power lead to some component leads that connect to an IO pin.

What you can do to narrow down the area of the fault

There are many components on the Nano board itself, by disconnecting everything else apart from power to Vin &amp; GND you can use the schematic to work out what voltages or signals should be present at various points and use a multimeter to test whether the expected voltages or signals are present.

For example you can test the input and output pins of the 5V regulator. You'd expect to see 12V at the input and 5V at the output. If you don't get 5V at the output, you might suspect the regulator has failed. You could check it's datasheet and see what kind of protections it has.

You could also check the voltage at the reset pin of the ATmega chip. What happens when you press the reset button?

And so on.

In the end though, it isn't worth spending much time on this. Your aim is not to repair the Nano but to avoid frying another one. Reading about failure modes and taking care with connections is probably the best.