Arduino UNO-R3 + Parallax RFID Read/Write Module

  pinMode(txPin, OUTPUT);     //pin 6
  pinMode(rxPin, INPUT);      //pin 8

You told SoftwareSerial that these were it's pins. Why are you now diddling with them?

What, exactly, did you connect between the Arduino and the RFID reader? Show a picture.

A status/error byte and a varying number of
data bytes will be returned depending on the command called.

Why don't you read this data?