Does your PC have a DB9 serial port, or are you using a USB to DB9 serial adapter?
If you loopback the serial port of the PC (connect Tx to Rx on the DB9) or the Rabbit (connect pin 1 to pin 6 on J11), are you able to see entered characters echo back? Checking the PC side would confirm you're opening the correct serial port.
Do you have the correct baud rate set on the Rabbit and PC? The sample defaults to 57600.
Did you configure the PC to not use any handshaking (no hardware or software handshaking)?