Vin doesn't light up led on nano

Hi,I am using an arduino nano to do some stuff with a led, and the project is meant to work powered by a 9V battery. When I plug the battery into the Vin and ground, or arduino light up but not the led attached to it.
However when I plug the arduino to my PC everything works fine.
Is this a lack of power or a problem with the arduino vin converter?

Thanks

When you say "Vin" do you mean the power input socket or the "Vin" pin?

Well that was the Vin pin. But I solved my problem. Actually I had a push button which was not using a pull-up resistor. And by a mean that I don't understand, I didn't switch the input states properly in the arduino. By adding a pull-up resistor everything worked fine. The problem was not from vin. Thx for your answer