Not sure why this transistor LED setup isn't working

I'm new to electronics and not sure why my setup isn't working. I've attached a schematic of what I think I have and the actual setup.

I'm confused about multiple things. First, in the picture with the original setup, I'm not sure why the LED is on without the arduino connected. I thought the transistor was supposed to act as a gate and not allow the circuit to run unless a digital signal from the arduino opens the gate.
Second, I have tried running this code:

void setup() {
  pinMode(5, OUTPUT);
}

void loop() {
  digitalWrite(5, HIGH);   // set the LED on
  delay(1000);              // wait for a second
  digitalWrite(5, LOW);    // set the LED off
  delay(1000);              // wait for a second
}

which I would expect to blink the LED on for 1 second and off for 1 second, but nothing happens when I run it.

I've tried using a new transistor in case I broke the one I was using, but it didn't help. I'm not sure what is going on here or what I am doing wrong.

I've tried multiple resistors between the arduino and transistor including a 100 ohm, 1k ohm, and now this 100k ohm one, but all have the same result.

Any suggestions?

You need a connection between the 12V supply ground and the Arduino GND. That may do it.

Steve

oh my god thank you so much!!!