If you really want to use serial, you might find that your computer motherboard does have a serial port, its just not connected to a D-sub socket. Mine for example has a row of 2x5 header pins (1 is N/C) on the motherboard that I used to add my own D-sub socket (sometimes the serial outputs are there as solder pads but without headers). Find out your make and model of motherboard then look for the "user manual" to see if there is a serial output anywhere.
Why not just buy a USB programmer?
If you dont already own a programmer or othr equipment requiring serial ports, this is the way to go as serial ports are slowly disappearing. just make sure that it is a USB programmer and not just a USB to Serial cable (the cable wont source the +12v required to put the PIC12F683 into programming mode)