NOR Gate is Working Correctly with Vcc Pin Disconnected
You've left out important details such as the part number and logic family of the NOR gate. By the sound of things you have an error in your Vcc connection but when that is removed the chip is able to power itself somehow - possibly through the internal input protection diodes - enough to switch the output as required.



TI application note Designing with Logic goes into detail for various logic families. Figure 5 shows from that document shows the input protection diodes. Note that if Vcc is not connected and one of the inputs is high then the whole chip could be powered up.