Arduino Uno - Serial Communication Problem

SoftwareSerial is obsolete. You should be using NewSoftSerial, instead.

  pinMode(rxPin, INPUT);
  pinMode(txPin, OUTPUT);

Do you want the software serial instance to manage these pins, or do you want to? It shouldn't be both ways.

  // toggle an LED just so you see the thing's alive.
  // this LED will go on with every OTHER character received:
  toggle(13);

That comment is plain wrong. The LED will be toggled every pass through loop, regardless of whether there was serial data read, or not.

  char someChar = mySerial.read();
  // print out the character:
  mySerial.print(someChar);

If nothing was available to read, mySerial.read() returns a -1. How do you fit that into a char? Why do you want to print garbage if there was nothing to read?