If the equipment at both ends of the network cable are switched off, then it cannot emit any form of interference.
Since you appear to have several TV points, it's more likely to be signal loss through the way in which each of the points derive it's splitting from the original aerial signal.
If the point with the problems is at the end of a distributed signal, it could have a relatively weak signal getting to it. As the original signal from the antenna will always deteriorate with time, due to water damage, corrosion, etc in the actual antennal, connection points/cable junctions, the weakest level at the end of a run can readily change from enough to give a good picture to too little. The same percentage loss of signal further up the chain may make no perceptible difference to a picture.
So - I would carefully check out the way in which the TV signal is distributed (do you/should you have a distibution amplifier) and the condition of ALL the cables and juctions in the system, from the antenna downwards - there's the most likely source of the problem.