New Arduino User

hi!, i’ve just recently bought an arduino mega 2560 R3, and i was dealing with it, trying to learn how to use it, but i think i have some troubles… when i was conecting my arduino to the USB port of my computer one of the 2 leds was blinking constantly, but then when i was uploading a example (SPACESHIPINTERFACE) it just stopped… then after about 2 or 3 minutes i decided to reset my arduino, but the led wasn’t blinking again… and i don’t know what to do…
Here’s the code for that example:

/*
  Arduino Starter Kit example
 Project 2  - Spaceship Interface
 
 This sketch is written to accompany Project 2 in the
 Arduino Starter Kit
 
 Parts required:
 1 green LED 
 2 red LEDs
 pushbutton
 10 kilohm resistor
 3 220 ohm resistors
 
 Created 13 September 2012
 by Scott Fitzgerald
 
 http://arduino.cc/starterKit

 This example code is part of the public domain 
*/

// Create a global variable to hold the 
// state of the switch. This variable is persistent 
// throughout the program. Whenever you refer to 
// switchState, you’re talking about the number it holds
int switchstate = 0;

void setup(){
  // declare the LED pins as outputs 
  pinMode(3,OUTPUT);
  pinMode(4,OUTPUT);
  pinMode(5,OUTPUT);

  // declare the switch pin as an input   
  pinMode(2,INPUT);
}

void loop(){

  // read the value of the switch
  // digitalRead() checks to see if there is voltage
  // on the pin or not  
  switchstate = digitalRead(2);

  // if the button is not pressed
  // blink the red LEDs  
  if (switchstate == LOW) {
    digitalWrite(3, HIGH); // turn the green LED on pin 3 on
    digitalWrite(4, LOW);  // turn the red LED on pin 4 off
    digitalWrite(5, LOW);  // turn the red LED on pin 5 off
  }
  // this else is part of the above if() statement. 
  // if the switch is not LOW (the button is pressed)
  // the code below will run  
  else {
    digitalWrite(3, LOW);  // turn the green LED on pin 3 off
    digitalWrite(4, LOW);  // turn the red LED on pin 4 off
    digitalWrite(5, HIGH); // turn the red LED on pin 5 on
    // wait for a quarter second before changing the light
    delay(250);
    digitalWrite(4, HIGH); // turn the red LED on pin 4 on
    digitalWrite(5, LOW);  // turn the red LED on pin 5 off
    // wait for a quarter second before changing the light
    delay(250);
  }
}

Moderator edit:
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tags added.

Try uploading the Blink example: File->Examples->01.Basics->Blink

Report what happens.

How did you wire it up exactly? Photo perhaps?