Arduino nano Serial port not recognized First sorry for my bad english, not my native lenguage.

Today I started working on my Arduino nano (first time used). When plugged for the first time the "L" led started blinking, after that I tried to write a simple program but I noticed that the "Port" option on the Arduino IDE was Gray. So I couldn't choose the port. After that I searched A LOT but nothing seems to work.

While trying to test if the problem was the Arduino and not the PC, I make a simple circuit with 1 LED, 1 resistor of 1Kohm, and a breadboard. I connected the 5V pin to the LED and GNG to the other point, And when I did this the "L" LED stopped blinking forever. I am 100%  sure that I did not make a short circuit. ¿Maybe the breadboard is in a bad state?

Additional info: 

-Windows 10.
-The port doesn't appear at Device manager (tried every port of my notebook).
-The "POW" led is ON when I plug the USB.
- The Arduino is a clone (chip CH340G).  

So now I don't know if the problem is the port or if the Arduino Nano is dead because of a possible short circuit between 5V and GND pins.

thanks in advance!
I think your Arduino got short or the transmitter-receiver in it is damaged so the device manager cannot recognize the COM port.It once happened with my Arduino Uno. Try changing the USB cable.If it does not help your Arduino is damaged.