You blew up the Nano's voltage regulator, due to
a) exceeding its voltage input range (look at the datasheet for Arduino Nano and it will tell you: not greater than 12V) -> ok, you obeyed the 12V, but a 12V battery comes with up to 15V ... (look at the datasheet of your battery)
most likely (or even dominated by) in combination with
b) drawing too much current at the same time and thus exceeding the voltage regulator's capablility to dissipate the heat which is caused by the voltage drop at the regulator multiplied by the current being drawn
To be sure, what exactly happened, pls post a complete and precise schematic of your constellation incl. all devices being wired to the Nano as requested here in previous replies.
After that we can calculate the power loss which the poor regulator on your Nano had to take and died from.
To give you a first idea, what will help your Nanos to survive (given that the overall current consumption won't exceed certain thresholds, which are determined by the Nano)
- If you could power it with a smaller voltage battery -> a 7V battery would do perfectly
- If you have to stay with that battery, you will have to lower the voltage input to a range of 7V..10V to be safe, which can be achieved by using a voltage step down converter.
This device will then be connected to the battery, its output (adjusted to a safe 7V) will power your Nano.
But - to be sure that this will work, a full picture of all devices in your configuration is needed to calculate the dimensions of the converter and make sure that there is no other issue in your project.