OK, lets go back a step.
You are verified the PC was talking and listening by shorting the pins on the DB9 connector, that's good. First, confirm that what you type is NOT echoed when you remove the short becuse there is a setting in Hyperterminal that copies the keyboard straight to the screen and I want to check you really are seeing data going down the cable and back again, not just locally echoed inside the PC.
After that, repeat your test but this time, remove the PIC and link together the connection that went to the TX and RX pins (pins 25 and 26 if you are using the DIP package). What I want to test is whether the data path right up to the PIC is working properly so we can eliminate an electrical fault. Again, without pins shorted you should not see anything you type appear on the screen but when they are shorted, everythng you type shuld appear. The PIC must be removed to do this test, you are only testing the circuits connected to the TX and RX pins at this stage.
Let me know what happens.
Brian.