What happens if you disconnect one of the green backlight wires?
The backlight turns off ;).
Now I changed the wires so everybody will be able to follow them 
I also added a "blink code" to verify the correct uploading--> it works! (the LED! not the LCD 
)
Here's the new code:
/*
LiquidCrystal Library - Hello World
Demonstrates the use a 16x2 LCD display. The LiquidCrystal
library works with all LCD displays that are compatible with the
Hitachi HD44780 driver. There are many of them out there, and you
can usually tell them by the 16-pin interface.
This sketch prints "Hello World!" to the LCD
and shows the time.
The circuit:
* LCD RS pin to digital pin 12
* LCD Enable pin to digital pin 11
* LCD D4 pin to digital pin 5
* LCD D5 pin to digital pin 4
* LCD D6 pin to digital pin 3
* LCD D7 pin to digital pin 2
* 10K resistor:
* ends to +5V and ground
* wiper to LCD VO pin (pin 3)
Library originally added 18 Apr 2008
by David A. Mellis
library modified 5 Jul 2009
by Limor Fried (http://www.ladyada.net)
example added 9 Jul 2009
by Tom Igoe
modified 8 Feb 2010
by Tom Igoe
This example code is in the public domain.
http://www.arduino.cc/en/Tutorial/LiquidCrystal
*/
// include the library code:
#include <LiquidCrystal.h>
// initialize the library with the numbers of the interface pins
LiquidCrystal lcd(12, 11, 5, 4, 3, 2);
void setup() {
// set up the LCD's number of columns and rows:
lcd.begin(20, 4);
// Print a message to the LCD.
lcd.print("hello, world!");
pinMode(13, OUTPUT);
}
void loop() {
// set the cursor to column 0, line 1
// (note: line 1 is the second row, since counting begins with 0):
digitalWrite(13, HIGH);
lcd.setCursor(0, 1);
// print the number of seconds since reset:
lcd.print(millis()/1000);
delay(500);
digitalWrite(13, LOW);
delay(500);
}
[edit]I found the Datasheet in the net. On the back of the LCD there is the "Code": YM2004A, so I searched for this code and found the Datasheet i posted in the link.[/edit]