I did not sort through the wiring. A schematic would go a long way here. The text version makes my head hurt.
Prior to getting into that lets make sure the PC is doing its job.
Unplug the RS232 cable from the PIC.
Type and you should see nothing.
Short pins 2 and 3 on the RS232 cable (it is still plugged into the PC but not the PIC target). To do this you can makup an DB9 with a wire soldered between 2 and 3.
With the jumper in place you should see what you are typing on the PC.
If this does not work either you did not follow these instructions or the BASIC program has problems. Maybe flow control problems. Others may have talked about that.