Can't send a signal to a NOR chip
You are powering the device through a 500 ohm resistor; you left one of the inputs of the NOR gate (pin 3) unwired while pin 2 is grounded. Always grounded - regardless of the state of the switch. So no changes will happen when you push the button.

This is what I think you made:







simulate this circuit &ndash; Schematic created using CircuitLab

Can you figure out what changes you need by looking at this? It should be pretty obvious... Hint - make sure both inputs of the NOR are connected to a level, and that that level changes in a way that changes the output when the button is pressed.

You probably want to have no series resistor in the Vcc of the NOR - instead, put a series resistor in line with the LED.

And since the truth table of a NOR is

A  B  C
0  0  1
1  0  0
0  1  0 
1  1  0


you will want the unused input at ground - then the used input needs to change state when the switch is pressed, so tie it (the currently open one) to the node between the switch and the LED.