6: Question about RFID-522 Reader

I wanted to do the "unlock the door using an RFID chip" trick. So I got a device from Sainsmart.

http://www.sainsmart.com/arduino/arduino-components/sainsmart-mifare-rc522-card-read-antenna-rf-rfid-reader-ic-card-proximity-module.html

Besides the sensor the package handily included one-each RFID keyfob- and credit card-type test devices.  I downloaded a library and sample sketch from the Internet, wired up the device and -- it didn't work. I downloaded a different library and sketch -- also didn't work. I was trying to test using the keyfob. Then I accidentally tested using the card. Worked! It had always worked.

I complained to Sainsmart and they eventually sent me a whole 2nd setup (new device, new fob, new card). Both cards work, neither of the fobs are recognized.

Anyone understand this problem?

Here's my sketch:

/*  Nano pins:
  RST: Pin 9
  SS: Pin 10
  MOSI: Pin 11 
  MISO: Pin 12 
  SCK: Pin 13  
*/  
#include <SPI.h>  
#include <RFID.h>  
#define SS_PIN 10  
#define RST_PIN 9 

RFID rfid(SS_PIN,RST_PIN);  
int serNum[5];

void setup(){  
  Serial.begin(9600);  
  SPI.begin();  
  rfid.init();  
}  

void loop(){
  int i;
  
  if(rfid.isCard()) {  
    if(rfid.readCardSerial()) { 
      for(i = 0; i <= 4; ++i) {
        Serial.print(rfid.serNum[i]); Serial.print(" ");
      }
      Serial.println("");  
    } else {
      Serial.println("nr");
    }
  } else {
   Serial.println("-");
  } 
  rfid.halt();
  delay(1000);  
}