TV Interference/RF Noise???

Hello, I have a problem with my TV. I recently hooked up my DVD to my new TV with component video cables and when the DVD is powered up I can see a "ghost" image of local TV stations floating across the screen. I have tried using two different "double shielded" component cables and it still occurs. I also tried both component inputs on the TV and the result was the same. I live in the city and I believe I am the victim of too much "broadcast noise" in my area (I'm in line of sight to the Sears Tower which has huge broadcast antennas on the roof). There also is an audible buzzing sound from the TV speakers. I originally thought this was a ground loop problem (the TV and DVD have no third ground prong on their plugs), but I have tried removing all other components from my AC outlets and I have also grounded my coax cable shield to my AC ground (this solved an earlier problem with my audio speaks buzzing when my amp was powered up). In fact the TV speakers still buzz when the coax is not connected to the TV at all and when I walk around to the back of the TV I can make the buzzing louder/quieter simply by being next to the rear of the TV. I have tried another TV in the same location and the speaker buzzing is still present. This leads me to believe that I'm picking up interference from the "airwaves" and it does not affect my HiFi because TVs are built poorly with cheap power supplies, poor shielding and improper grounding. Can anyone suggest a solution? How can I get the "ghost" image to disappear when I use the component video cables? Can I shield the TV somehow to stop the speaker buzzing? Should I ground the TV frame to my AC ground? Thanks for any advice in advance.

-DAVE