Certainly could be a grounding issue. Specifically, it sounds like something on the CNC is not properly grounded and is connecting to ground through the PC.
If you have a multimeter, leave the RS-232 cable connected at only one end (either PC or CNC) and leave the other end disconnected. At the disconnected end, check for any voltage between the metal housing of the serial connector and the PC/CNC. Ideally, there should be no voltage. Check for both DC and AC voltage. I have seen machines in the field with as much as 30VAC between the machine and the PC.