strange serial sending problem

i tried to make some code but i have a problem. First i made it some easier :

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

void loop() {
  Serial.println("hallo");
  delay(1000);
}

That works perfect, i recieve every second "hallo" and the TX led blinks. But when i disconnect my arduino and connect it again, i don't see the TX led blinking, and when i open serial monitor .Then TX led start blinking. Do i make a fault or do i missing something?

You should find if it is the usb or the processor that is malfunctioning. Try this:

void setup() {
   Serial.begin(9600);
   pinMode(13,OUTPUT);
}

void loop() {
  Serial.println("hallo");
  digitalWrite(13,HIGH);
  delay(1000);
  Serial.println("bye");
  digitalWrite(13,LOW);
  delay(1000); 
}

Disconnect, then reconnect the Arduino. If the onboard pin 13 LED is on for a second and off for a second over and over, the code is still running. If not, the code has failed.

the leds(pin 13) is working but the tx one not. I tried that before with a pushbutton, when i push, the led goes on en he send some serial code(without TX blinking).