All color monitors and televisions have degaussing coils built-in because the picture tube's shadow mask gets slightly magnetized by external sources very easily. The picture can be quite horrible. If the degaussing coil on your set blows the chassis fuse, then there is something wrong with either the degaussing circuit on the chassis or the coil itself. This is usually caused by a faulty degauss posistor/thermistor, or the coil is shorted.
You can use a manual degaussing coil to clear up the problem on the bench, but the picture will become discolored the next time the monitor is moved (the earth's magnetic field affects it too).
Don't use strong permanent magnets to try to clear up the problem. You risk bending the shadow mask inside the tube. If you damage this, then there is no fixing the tube. To degauss a tube you need an *alternating* magnetic field - not a fixed one.
Lacking a degaussing coil, you can use a large soldering gun held near the face of the screen with the trigger held down, a handheld bulk tape eraser, an electric drill, or some other source of an alternating magnetic field. You can also use the coil from a junked TV set, powered directly from the mains (just be careful, it'll heat up fast!).
-Ian