1) Are you sure you have pin 2 correct and pin 5 correct (you are using a 9 pin connector that is straight thru?) see http://www.airborn.com.au/rs232.html

2) Try it without TX connected

3) A must - add a decoupling capacitor across VDD and VSS (10 uF should do or anything close to this)

4) You do have pin 5 connected to your PIC ground?

5) try another power supply that can be regulated (or 3 AA batteries in series)

6) Do you have access to an oscilloscope? see what is coming out of PortA.1 and pin 2 on the cable?

7) Check your hyperterminal settings to make sure you have 300 selected and the parity off

8) you have been using a crystal like in your sketch?

report back