LCD shows output without pressing the sensor
First off I edited indentation in your code because incorrect indentation is little bit confusing.

#include &lt;LiquidCrystal.h&gt;
LiquidCrystal lcd(13,12,11,10,9,8);
#define vibrate_sense 7

char str[70];
char *test="$GPGGA";      
char logitude[10];
char latitude[10];

int i,j,k;
int temp;
//int Ctrl+z=26;    //for sending msg
int led = 13;


void setup(){
  lcd.begin(16,2);
  Serial.begin(4800);

  pinMode(vibrate_sense, INPUT);
  pinMode(led, OUTPUT);

  lcd.setCursor(0,0);
  lcd.print("..Initializing..");
  lcd.setCursor(0,1);
  lcd.print("....System...");
  delay(1000);
  lcd.clear();
  lcd.setCursor(0,0);
  lcd.print("Searching for");
  lcd.setCursor(0,1);
  lcd.print("Gps Signals");
  delay(2300);
  lcd.clear();
  lcd.setCursor(0,0);
  lcd.print("Setup Completed");
  delay(500);
  lcd.setCursor(0,0);
  lcd.print("Accident detect");
  lcd.setCursor(0,1);
  lcd.print("&amp; Alert system");
  delay(1500);
  lcd.clear();
  lcd.setCursor(0,0);
  lcd.print("No accident");
  lcd.setCursor(0,1);
  lcd.print("occured");
}


void loop(){
  if (digitalRead(vibrate_sense) == 0){
    for(i = 18; i &lt; 27; i ++){          //extract latitude from string
      latitude[j]=str[i];
      j++;
    }

    for(i=30;i&lt;40;i++){          //extract longitude from string
      logitude[k] = str[i];
      k++;
    }

    lcd.clear();
    lcd.setCursor(0,0);        //display latitude and longitude on 16X2 lcd display 
    lcd.print("Latitude(N)");
    lcd.print(latitude);
    lcd.setCursor(0,1);
    lcd.print("Longitude(E)");
    lcd.print(logitude);
    delay(500);
    lcd.clear();
    lcd.setCursor(0,0);
    lcd.print("Accident has");
    lcd.setCursor(0,1);
    lcd.print("been Detected");
    delay(500);
    lcd.clear();
    lcd.print("Sending SMS");
    delay(500);
    lcd.clear();
    Serial.begin(9600);

    Serial.println("AT+CMGF=1");    //select text mode
    delay(10);
    Serial.println("AT+CMGS=\"7066128969\"");  // enter receipent number
    Serial.println("Vehicle Accident occured:");
    Serial.print("Latitude(N): ");             //enter latitude in msg
    Serial.println(latitude);                  //enter latitude value in msg
    Serial.print("Longitude(E): ");            //enter Longitude in Msg
    Serial.println(logitude);                  //enter longitude value in msg
    Serial.print("http://maps.google.com/maps?&amp;z=15&amp;mrt=yp&amp;t=k&amp;q=");
    Serial.println(latitude);
    Serial.println("+");
    Serial.println(logitude);
    Serial.write(26);                      //send msg  Ctrl+z=26

    lcd.setCursor(0,0);
    lcd.print("SMS Sent");
    delay(1000);
    lcd.clear();
    lcd.setCursor(0,0);
    lcd.print("Help Please");

    temp = 0;
    i = 0;
    j = 0;
    k = 0;
    delay(20000);                        // next reading within 20 seconds
    Serial.begin(4800);
  }
}

void serialEvent(){
  while (Serial.available()){            //Serial incomming data from GPS
    char inChar = (char)Serial.read();
    str[i] = inChar;                    //store incomming data from GPS to temparary string str[]
    i++;
    if (i &lt; 7){
      if(str[i-1] != test[i-1]){         //check for right string
        i = 0;
      }
    }
    if(i &gt;= 60){
      break;
    }
  }
}




Second thing is this line if (digitalRead(vibrate_sense) == 0){ you are checking there vibrate_sense for value 0. Are you sure, that triggered value is 0 and not 1? Try this code to test which value is equal to triggered state.

#define vibrate_sense 7


void setup() {
  Serial.begin(9600);
  Serial.println("Sensor testing");
  pinMode(vibrate_sense, INPUT);

}

void loop() {
  Serial.println(digitalRead(vibrate_sense));
  delay(300);
}




Last thing is connection of your sensor/button. For button you have to use also PULL_UP/PULL_DOWN resistor to have correct logic value on digital pin.