You've melted the leads to the cigarette lighter (due to overheating, and now the burnt insulation has exposed the wiring. The ground wire is probably fine, but the hot wire is exposed and in contact with something else metallic, causing the fuse to immediately trip upon replacement.
You will have to remove the head unit to get to the harness, and then disconnect the cigarette lighter connection altogether. If the fuse doesn't blow this time, then check the connection first, then start tracing from there.
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