Well, I replaced the shoe and got the noise back. Following the directions of some forum members I noticed that unplugging the coaxial cable (cable TV) from the LCD stops the noise, so I guess it`s a problem with the ground of the cable TV.
PS: I called my cable company and the engineer said that this was a common problem with digital appliances, and that a solution might be connecting a separate grounding copper rod to any metal part of the appliances. Would this work ? Sort of creating a dedicated ground for the system.