And I don't know your hardware - but. You can't run the output of a PC serial port directly into a hardware serial port of a PIC, even with a resistor. The PC output is LOW when no character is transmitted, while the PIC expects a HIGH when no character is transmitted. If you use a level-shifter/inverter like a MAX232 between your PIC and PC, you don't need a resistor (pull-up or otherwise), and the inversion will be taken care of for you.