Serial Port & GSM Modem Problem

Hi All,
I am having a bit of a problem with receiving data from the serial port (pin 0&1). I am trying to communicate with an external modem (Telit). I did connect Arduino (RX) to Modem (TX) And Arduino (TX) to Modem (RX). When I connect the modem to the PC, everything works fine the modem is responding with OK and I am able to send SMS. Can I connect the Modem to pin 0&1 and still use the USB to write debug messages? And can anyone please point me in the correct direction?
Thanks in advance!
Pieter
Some code I tried but is not working.

#include <LiquidCrystal.h>

LiquidCrystal LCD(12, 11, 5, 4, 3, 2);

int incomingByte = 0;
#define INLENGTH 16
#define INTERMINATOR 13
char inString[INLENGTH+1];
int inCount;
int i = 0;

void setup(){ 
  // Initialize LCD 
  LCD.begin(16, 2);
  LCD.clear();
  LCD.setCursor(0, 0); 
  LCD.print("LCD STARTUP");  
  // Initialize Serial Port
  Serial.begin(115200);
  delay(5000);
  Serial.println("AT+CMGF=1"); 
  LCD.setCursor(0, 1); 
  LCD.print("INITIALIZE DONE."); 
  delay(1000);
}

void readSerial(){
      if (Serial.available() > 0) {
            inString[inCount] = Serial.read();                      
                inCount++;
                    }
    if (inString [inCount] == INTERMINATOR) {inCount = 0; LCD.clear(); i = 0;}

    while (i <= inCount){    
      LCD.setCursor(i, 0);    
      LCD.print(inString[i]); 
      i++;
    }
    delay(300);
}

void loop()
{
  Serial.println("AT");
  delay(300);
  readSerial();
}

Some code I tried but is not working.

In what way does the code not work?

Be carefull, if thats an external modem that can connect directly to the pc then it uses RS232 and not TTL serial voltages, you may need to convert using a max232 type chip.

Also the serial port on the Arduino 0,1 pins are used for the serial connection to PC so you may need to use a softserial library on other pins to get the modem and PC connection working simultaneously..

See http://www.arduino.cc/en/Tutorial/ArduinoSoftwareRS232

EDIT: This writeup describes connecting an Arduino to a computer via RS232 but you can connect to any RS232 device with the same setup ..
From experience I would also suggest setting the modem communication rate to some fixed value via the computer and AT command (see modem manual). The modem may otherwise struggle to determine the connection speed you want to use from the Arduino.