Arduino Nano Fried on Music Reactive Led Strip
I assume you are powering the Nano through VIN or USB, and you are then powering the LED strip from the Nano's 5V pin.


From the 12V battery the current flows through an LM1117 linear voltage regulator. Draw too much current (>800mA) and it will overheat and either shut down (if it's a good one) or melt (if it's an inferior Chinese clone).
From USB the current flows through an SS1P3L diode with a maximum rating of 1.5A. If you draw more than that you will blow the diode and the board will appear dead.


So basically you're drawing too much current.

The proper way of powering a setup like this is:


USB connection to power the Arduino only
12V into a 5V switching ("buck") regulator rated for at least the maximum current the LED strip needs
5V switching regulator into the LED strip directly
Connect the ground of the 5V to the ground of the Arduino


or


12V into a 5V switching ("buck") regulator rated for at least the maximum current the LED strip needs
5V switching regulator into the LED strip directly
5V switching regulator also to the 5V (and ground) pin of the Arduino to power the Arduino


or

As above but with a 5V power supply instead of the 12V and switching regulator

Note that it is important that your supply can provide you with at least as much current as the peak current your system will need.  If that is a problem then you can split the LED strip into chunks and power each chunk separately from a lower current supply.