Connecting 12V fan and 3V LED to 9V batteries and drawing more power
It seems that you are trying to connect the led directly to the 12V thereby reducing the voltage due to the internal resistance of the two batteries. That is not the way.
Remenber also that 2 batteries of 9 V can make the ventilator turning but also there the voltage will drop.
If this is the case place a resistor in series with the led. Let us say
put some 560 ohm in series with the led and try again. It is better to look for a proper 12V supply.