Degaussing a tv
A TV form 6 years ago almost certainly has a thermister in series with the degaussing coil control. It works like this;
1) when power has been off for a while, the thermister is at room temperature.
2) when the set is turned on, the cold thermister allows a large amount of current to flow in the degaussing coil, thus degaussing the picture tube.
3) the thermister quickly heats up, and as its temperature rises, so does its resistance.
4) In a second or two, the thermister will reach its point of equalibrium. The current flow through it will maintain its temperature. This current is very low, so the coil is barely energized.
5) When the set is turned off, the current flow stops, and the thermister cools.
Most of the time, the thermister burns up. Sometimes, the coil wires break, it's rarely anything else.
A word of caution, if you go poking around in the back of a TV, there are capacitors that can store a lethal charge, even if the set has been off for several days. Stay away from the thick wire that goes to the screen side of the picture tube, usually on top. It operates at about 1000 volts per inch of tube size.
P.S. A TV tech can troubleshoot and fix this pretty easily.