I may think of few things here
1) 9600 baud with internal osc is a bit dangerous, try at lower baudrate
2) internal OSC calibration is screwed up.
3) all multiplexed analog stuff are not disabled
4) there's no max-232 (or else inverter) between the PIC and the PC
5) noisy supply line
6) maybe something else

i'm doing a little something here, i'll post it later so you could try on your side as well