Two buttons - one output

Problem solved! Using hardware that actually works - plus code recommended by the Forum. Thanks again for helping out.

/*
  TWO BUTTONS  -  ONE OUTPUT
 
 Turns on a light emitting diode(LED) when pressing one pushbutton;
 and off again when pressing a second button. LED stays on in between.  
 
 The circuit:
 * LED attached from pin 13 to ground 
 * pushbuttons attached to pins 2 and 3 with 10k pull-down resistors to ground.
 
 Written 2/1/13 by
 Telefondreng.
 */

// constants used to 
// set pin numbers:
const int button1 = 2;     // the number of the 1st pushbutton pin
const int button2 = 3;         // the 2nd
const int ledPin =  13;      // the number of the LED pin



void setup()
{
  // initialize the LED pin as an output:
  pinMode(ledPin, OUTPUT);      
  // initialize the 1st pushbutton pin as an input:
  pinMode(button1, INPUT);   
  //initialize 2nd pushbutton
  pinMode(button2, INPUT);
  
  digitalWrite (ledPin,LOW);
  
}

void loop()
{ 
  if ( digitalRead(button1))
    {
      digitalWrite (ledPin,HIGH);
    }  
  if (digitalRead(button2))
    {
      digitalWrite(ledPin,LOW);
    }  
 }