The datasheet says 7412 has open collector outputs. That means the output of the gate can only pull down (GND), it can not pull up (to Vcc).
You need a resistor to V+ for each gate output pin (6, 8, 12)
Alternatively, for testing you can connect the LED to the Vcc instead of GND (with LED anode to Vcc), so you won't need extra resistors for each gate output.