Just trying to find out if my Arduino UNO R1 board is broken or not.

First of all, everything seems normal, Arduino board shows "on" (green) when I plug it on my computer, I also can verify and upload programs to my Arduino board. But, no matter what program I upload the pin 13 turns on and off 3 times and that's it. I'm checkin it by using a LED. Eg. if I want to use another pin (ex. 7, 8, 12) it doesn't work, or even to write a program for turning on/off 9 times pin 13 doesn't work...

Note: I noticed that pin 8 turns the LED for less than a 1/2 a second.

I already tried to restart board by bridging the reset pin and also by pushing reset directly on the board, I also reinstalled Arduino Genuino Application. I thought to update Atmega8U2 firmware but accordingly to Arduino site I don't need to update since I have firmware rev. 0.01.

It would be also great not to have to buy a new Arduino UNO. Thanks for your help

Edit: Here is how I'm trying to make pin 12 work

int ledPin = 12;

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

void loop()
{
    digitalWrite(ledPin, HIGH);
    delay(2000);
    digitalWrite(ledPin, LOW);
    delay(2000);
}