Problems for using RFID-RC522 with Arduino

I am a newbie for using Arduino. I bought a RFID reader (RFID-RC522) and connected it with Mega 2560. I have installed the library and after connecting it, i can't see anything in the serial monitor after putting RFID tags on the reader.It is supposed to read the serial number of each tags and show it on the serial monitor. just don't know why and hope someone can provide me some solutions. Here is my pin connection and my code:

RC522-->MEGA 2560:

SA(1) -> SS(digital Pin 53)
SCK(2) -> SCK(digital Pin 52)
MOSI(3) -> MOSI(digital Pin 51)
MISO(4) -> MISO(digital Pin 50)
(5) not connected
GND(6) -> GND
RST -> (digital Pin 34)
+3.3V-> +3.3V

I can't insert my code in here because it exceeds the maximum allowed length. Therefore I 've upload the code.

ED RFID RC522 module arduino code.pde (20.1 KB)

I bought a RFID reader (RFID-RC522)

Your "link" doesn't work,

I have installed the library

Which one? From where?

const int chipSelectPin = 10;

But, you connected the chip/slave select pin to 53.

   Serial.begin(9600);                       // RFID reader SOUT pin connected to Serial RX pin at 2400bps

When the comment and the code disagree, the code is right. Is the code right for your reader?

WHY is the reader connected to the same serial port as the PC?

Or, is the comment pure crap?

  pinMode(NRSTPD,OUTPUT);               // Set digital pin 10 , Not Reset and Power-down

This isn't doing anything to pin 10.

                        //Serial.println("The card's number is  : ");
			//Serial.print(serNum[0]);
                        //Serial.print(" , ");
			//Serial.print(serNum[1],BIN);
                        //Serial.print(" , ");
			//Serial.print(serNum[2],BIN);
                        //Serial.print(" , ");
			//Serial.print(serNum[3],BIN);
                        //Serial.print(" , ");
			//Serial.print(serNum[4],BIN);
                        //Serial.println(" ");

I wonder why nothing appears on the serial monitor. Uncomment all this stuff to find out what is happening, if anything.

All the things I saw is from this website: https://gergely.imreh.net/blog/tag/arduino/ and that website provided the code is from How to get started with the Mifare MF522-AN and Arduino – Grant Gibson . It said it can work well with MEGA 2560 although the wiring of the source code is for Uno.