Connecting 2 arduino boards together.

Hi, I'm trying to connect 2 Due's using the tutorial "Arduino to Arduino Serial Connection" -> Arduino to Arduino Serial Communication | Robotic Controls. I get the Physical pixel tutorial to play on one board connected to one computer but when I connect the other Due to a different computer and put this code in :

void setup() {
  Serial.begin(9600);
}

void loop() {
  Serial.print('H');
  delay(1000);
  Serial.print('L');
  delay(1000);

It says "No device on COM4" This only happens when I connect both the TX and the RX from one board to another. What can I do to fix this.
Thanx

Do not connect them together during upload of code because the other arduino is swampling the signal from the USB and so the computer things there is nothing connected.