It depends on the pattern of the picture defects. If you could describe what goes on exactly and the way it varies from turn on to turn off and if it remains constant, fluctuates, etc. and what happens
It is more likely to be the convergence circuit that has gone bad. But, it requires some testing to be sure. If it is the convergence it will not require a new board but does require replacing two integrated
It will require some testing to be sure. But, I think it is a power supply failure. It will require replacement of one or two electrolytic ripple reducer capacitors. The cost of repair will be around
But, does the thumping sound stop when the volume is reduced to zero? IF NO: The problem may be what is called "motorboating" and is mostly caused by an instability from the power supply that is feeding
Can't really help you much without more information. Make and model of car and system. I don't compute with the term "compact stereo system in my car" because compact stereo is a term used in home systems

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