I've had a little experience with a plasma causing one of my PC's to reboot. I'd say that the motherboard had a design weakness that made it susceptible to the RF noise.
Best to try a different PC. Before you actually go to all the work of changing over the PC in your control, you can just set up the prospective PC near the same location, and fire up the plasma and see how the PC reacts.
Run the PC through a battery backup type UPS (surge protector). You should already be doing this.