Arduino Nano LED not working
As your program is currently written, you should see your LED light. I see nothing wrong with your program or your wiring. I am also assuming that you had no errors while compiling and downloading the program.

With the rest of the lines uncommented, what you should see is your LED light up for 1.5 seconds and then off. Then after another 1.5 seconds, the on-board LED should turn on and then off (both 1 second).

If you have wired up the LED wrong (or a bad connection), you should at least still see the on-board LED flash about once every 5 seconds. If you don't see this then something else is wrong.

One thing I notice from the photos is that you have no way of powering your circuit. (I realise this may just be while you took the photo). Plug a USB cable into the Arduino and the other end into the computer. You should see the LED called "POW" light up.  

To verify your LED circuit, try disconnecting the jumper at D12 and connecting it to 5V and you should see the LED light. If this works then your circuit is OK so replace the jumper back at D12.

If the LED still does not light up when the jumper is connected to 5V then we need to dive into that circuit. Possible reasons include:


The LED is dead -> replace the LED
The breadboard is not making good connection -> wiggle the leads (to scratch away any corrosion) or twist together the wires where possible or even solder them together.
The jumper wires are manufactured poorly (eg. the plastic wasn't stripped before crimping) -> check the jumper crimps.
The LED has been manufactured wrong and what should be the anode is actually the cathode (I have seen this) -> reverse the polarity of the LED.
The resistor is burnt out -> replace the resistor.