Issue while connecting ESP8266 with Arduino Mega. It always says “Module have no response.”

I took your code as a starting point and got it to work with some small modifications. I am providing my version below for your review. I had to add a bunch of delays. I am also communicating with the ESP8266 at 19200 baud.

I have not optimized the timing yet but I was able to run this code for 24 hours straight with no issues. I am using Pins 6 and 7 on the Arduino for COMM to the ESP8266.

#include <SoftwareSerial.h>
#define SSID "YOURSSID"
#define PASS "YOURPW"
#define DST_IP "220.181.111.85"

SoftwareSerial Serial2(6, 7); // RX, TX

void setup() {

// Open serial communications w ESP8266
Serial2.begin(19200);
Serial2.setTimeout(5000);

// serial 0 is to usb
Serial.begin(115200);
while(!Serial); 
while(!Serial2);

Serial.println("ESP8266 Demo on Mega2560");

while (Serial2.available() > 0)
Serial2.read();
delay(1000);
while (Serial2.available() > 0)
Serial2.read();

//test if the module is ready
Serial.println("RESETTING ESP8266 WIFI CHIP");
Serial2.write("AT+RST\r\n");
delay(2500);
while (Serial2.available() > 0)
Serial.write(Serial2.read());

delay(2500);
while (Serial2.available() > 0)
Serial.write(Serial2.read());
Serial.println("");

//  connect to the wifi
boolean connected=false;
for(int i=0;i<5;i++) {
if(connectWiFi())
{
connected = true;
break;
}
}

if (!connected){
Serial.println("Not Connected.");
}

Serial2.println("AT+CIFSR");
delay(2000);
while (Serial2.available())
Serial.write(Serial2.read());
delay(2000);
while (Serial2.available())
Serial.write(Serial2.read());

//  set the single connection mode
Serial2.println("AT+CIPMUX=0");
delay(2000);
while (Serial2.available())
Serial.write(Serial2.read());
delay(2000);
while (Serial2.available())
Serial.write(Serial2.read());
}

void loop() {

String cmd = "AT+CIPSTART=\"TCP\",\"";
cmd += DST_IP;
cmd += "\",80";
Serial2.println(cmd);
Serial.println(cmd);
delay(5000);

if(Serial2.find("Error")) return;

cmd="GET / HTTP/1.0\r\n\r\n";
Serial2.print("AT+CIPSEND=");
Serial2.println(cmd.length());
delay(2000);

if(Serial2.find(">"))      {
Serial.print(">"); 
}
else {
Serial2.println("AT+CIPCLOSE");
Serial.println("connect timeout");
delay(2000);
return;
}
Serial2.print(cmd);
delay(2500);

while (Serial2.available()) {
char c = Serial2.read();
Serial.write(c);;
if(c=='\r') Serial.print('\n');
delay(5);
}

Serial.println("");
Serial.println("====");
delay(2000);
}

boolean connectWiFi() {

String cmd;
int iIP;

iIP = 0;
Serial2.println("AT+CWMODE=1");
delay(5000);
while (Serial2.available())
Serial.write(Serial2.read());

cmd="AT+CWJAP=\"";
cmd+=SSID;
cmd+="\",\"";
cmd+=PASS;
cmd+="\"";

Serial2.println(cmd);

delay(2000);
Serial.println("Line 1");
while (Serial2.available() > 0)
Serial.write(Serial2.read());

delay(2000);
Serial.println("Line 2");
while (Serial2.available() > 0)
Serial.write(Serial2.read());
if (Serial2.find("OK")) {
Serial.println("WIFI OK was received!");
iIP = 1;
}  

if( iIP == 1 ) {
Serial.println("OK, Connected to WiFi.");
return true;
}
else  {
Serial.println("Can not connect to the WiFi.");
return false;
}

}

Your transmitter and receiver pins need to be crossed, rx->tx and tx->rx. As a mnemonic, the two ends of the antenna point to the board edge with the receiver pin and it is that pin that needs the voltage divider. While you're at it, it would be a good idea to tie the RST pin high, as well as the CH_PD. I use one 10K pullup for both.

Recent versions of these boards are shipped with their baud rates set to 115200. Since you're using a hardware UART on the Mega board, you can send/receive to it at that rate.

Note to readers using a software UART (SoftwareSerial): First thing, change the board's baud rate to 9600 and communicate with it at that rate. You can use SoftwareSerial to make the change as it sends at 115200 reasonably reliably, but its receive function can't keep up at that rate).

You can confirm your connections and baud rate with:
EspSerial.println("AT");
You should receive `OK' in reply.

You have connected to serial1 and in the program, you have called Serial2.