This probably won't be helpful, but whenever someone inquires about trouble with a Realtek network chipset someone ALWAYS responds that Realtek network hardware is junk and that you should replace it with something good, such as an intel e100 or e1000 or some such.
Me, I've never had trouble with a realtek card, myself.
Fred - thanks - but not an option in this case. Its built in and no slots available.
jerry