TC35 GSM module does not respond to "AT" command

Still the same problem... :~
I can not go in this part of the loop:

if (gsmSerial.available() > 0)
{
  Serial.write(gsmSerial.read());
}

Ground of the TC35 module is connected to the ground of the Arduino...

The TC35 module is powered by a adjustable power supply witch is set to 5V DC & max 1A.

On the display of the power supply i can see the current swing between 20 - 80 mA...