why do you say that your house has no ground wiring?
ground only one outlet is a massive waste of money, also doesn't protect your house and the people living it it
remember that a proper grounding is there to protect persons inside the house in the case of a faulty device, not just protect your new shiny pc
in the case of electricity flowing to where it shouldn't, to a person, it flows to the ground doing no harm, the grounding is a must, what you need to determine is when you are going to check with a electrician how good is the grounding, what improvements can be done and why you believe that the sockets doesn't have proper grounding
last time i saw a complain like this i discovered in another house that the house indeed had proper grounding but the idiot installing the wall sockets didn't screwed the ground line in the socket, genius!