Since your printer is rather old and only has parallel port, you need to get a parallel to USB printer converter first. Then you can connect printer to one of your PC. Connect both PC to router. The PC without printer can use the printer through the other PC. The drawback is that the PC connected with printer has to be on all the time.
The other option is to get a printer sever if your router does not have one. This allows either PC to use printer independently.
The cost really adds up. Consider updating your hardware instead as suggested by others.