Thanks for your answer 
D'oh ! Chrome have closed (?!), I have to write everything again... so :
Then, your Arduino is broken.
I don't think so, it works fine by connecting the arduino in the computer without the Xbee module. And the Xbee modules work, because I tried tho switch them and the problem is still the same (so that is not a module that is only able to receive and not to send).
There are no RSSI LEDs to light up... There is an associate LED that blinks to indicate that the XBee is operating, and blinks at a different speed to indicate that it is paired.
The modules get correctly associated, and the associate LED blinks on both Xbee. But the RSSI LED light up for a second when associating. I've found on web that it's quite normal.
You need to post a link to the XBee shield you have. There are no such jumpers on either of the 2 shields I have.
I haven't USB/Xbee jumper, but I have a RS485/RS232 jumper. My shield is this one :
Post your code, too. Also, what kind of XBees do you have? Series 1 or Series 2/2.5?
I've got 2 Xbee Series 2/2.5 (now, I know that it was an error to buy 2.5 instead of 1 to set up a point to point networks).
My code is the PhysicalPixel with the Serial.println added :
const int ledPin = 13; // the pin that the LED is attached to
int incomingByte; // a variable to read incoming serial data into
void setup() {
// initialize serial communication:
Serial.begin(9600);
// initialize the LED pin as an output:
pinMode(ledPin, OUTPUT);
}
void loop() {
// see if there's incoming serial data:
if (Serial.available() > 0) {
// read the oldest byte in the serial buffer:
incomingByte = Serial.read();
// if it's a capital H (ASCII 72), turn on the LED:
if (incomingByte == 'H') {
digitalWrite(ledPin, HIGH);
}
// if it's an L (ASCII 76) turn off the LED:
if (incomingByte == 'L') {
digitalWrite(ledPin, LOW);
}
}
Serial.println("Hello World !");
}
When connected to the computer using serial, everything is fine. I can play with the LED using H & L, and I receive a bunch of Hellos.
When using Xbee modules, H & L works, but I do not receive any Hello. IMHO, it seems that the serial connection isn't well established.
Have a nice day !
Edit : I think it come from the beginning of the serial connection : when the arduino is plugged into a computer, it doesn't send the bunch of hellos (the tx doesn't light up). It starts to send hellos when I start the serial monitor. So I think it doesn't send hellos over Xbee because it doesn't detect that serial monitor has been launched (no correct serial initialization over radio ?), or something like that ?