Bluetooth communication with computer using SoftwareSerial

I have a Compact Mega 2650 with the JY-MCU Bluetooth module. I have the BT module connected to pin 2 and 4 (Rx and Tx on the JY-MCY, Tx and Rx defined on SoftwareSerial). All that I want is to write something on the Mega and read it on the computer. The computer and the JY-MCU pair with no problem, and I open a serial terminal and connect to the BT port at 9600 baud to read what the arduino sends. I am running the following code on the Mega:

#include <SoftwareSerial.h>

const int rxPin = 4; //SoftwareSerial RX pin, connect to JY-MCY TX pin
const int txPin = 2; //SoftwareSerial TX pin, connect to JY-MCU RX pin
                     // level shifting to 3.3 volts may be needed

SoftwareSerial mySerial(rxPin, txPin); // RX, TX

const int ledPin = 13;  // led pin

int state = 0;        // if state is 1, the LED will turn on and
                      // if state is 0, the LED will turn off
int flag = 0;         // a flag to prevent duplicate messages

void setup() {
    // sets the pins as outputs:
//    pinMode(ledPin, OUTPUT);
    mySerial.begin(9600);
//    digitalWrite(ledPin, LOW); // LED is initially off
}

void loop() {
    //reads serial input and saves it in the state variable
    if(mySerial.available() > 0){
      mySerial.println("1234");
      delay(1000);

        }
    }

I get nothing at all back. Any ideas on how I can approach debugging this? Is there an obvious problem with the code? Thanks for the help.

Bret

const int rxPin = 4; //SoftwareSerial RX pin, connect to JY-MCY TX pin
const int txPin = 2; //SoftwareSerial TX pin, connect to JY-MCU RX pin
                     // level shifting to 3.3 volts may be needed

SoftwareSerial mySerial(rxPin, txPin); // RX, TX

The Mega has 4 hardware serial ports. Why are you using SoftwareSerial?

Have you looked at the documentation for SofwareSerial? Specifically, have you noted which pins can be used for SoftwareSerial on the Mega?

Using the hardware UART took care of it. I was using SoftwareSerial mainly because that was what was used in the examples that I found. Thanks for the help.

Updated Code:

void setup() {
    Serial1.begin(9600);
}

void loop() {
    {
      Serial1.println("5678");
      delay(1000);
        }
    }