Bouzy,
Looks like you are trying to make a racing light... I assume the other pins you are sending HIGH are turning on some LEDs.
There actually is no problem with your code if you had the right buzzer. Some buzzers "self-oscillate" at a particular frequency, and some need to be stimulated at a frequency to produce a sound. It should be obvious by now that you have the kind you need to stimulate 
Based on your buzzer's specs, I would change your resistor from 470ohms to 100ohms. Make sure it's at least a 1W resistor. 2W would be better, but you are only turning it on for 3 seconds so it shouldn't get too hot in that period of time. This will drop the 12V down to 3.5V for your buzzer, since it has a coil resistance of about 42ohms. (12V * 42 / (100+42)) is about 3.5V.
Given that you are driving it correctly now, you need to "stimulate" it.
If you replace this code:
digitalWrite(buzzPin, HIGH);
delay(3000);
With this code:
for (long i = 0; i < 2048 * 3; i++ )
{
// 1 / 2048Hz = 488uS, or 244uS high and 244uS low to create 50% duty cycle
digitalWrite(buzzPin, HIGH);
delayMicroseconds(244);
digitalWrite(buzzPin, LOW);
delayMicroseconds(244);
}
You should hear a 2048Hz tone on your buzzer for 3 seconds.
You can also put this code at the end of your loop() routine to keep it from looping over and over:
while(true); //kill loop, while true do nothing
Here's a couple links to some code that may help:
Hope that helps! I had fun testing the code so it's all good on my end 
-Brett