TC35 GSM module does not respond to "AT" command

Using Arduino Networking, Protocols, and Devices
6

Although the the checking of available character is perform after 5 s, there could be possibility that the character comes in after 5 s although it's rather unlikely. In that case, you serial check will return zero.
Why not doing something simpler like this:

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

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

Whatever you type on the PC should be relayed to the modem and vice versa.
If this fails, it could be something simple like inadequate current of the power supply or a GND is not connected between the boards.