Unable to connect and configure ESP8266 wifi module with Ardunio Mega
Your ESP8266 module is most likely fried now, if your wiring diagram is any indication of your actual hardware setup.

The ESP operates at 3.3V, which means that every pin on it can receive no more than 3.3V as input. And it looks like you've directly connected the ESP's TX pin with the Arduino, without using a level shifter. The Arduino GPIO pins work on 5V logic levels.

Test this module out with a level shifter (resistor divider network, 3.3V zener, level shifter IC; pick your poison). If the ESP still doesn't respond, swap it out with a new one and repeat.