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It was probably just a bad plug adapter (bad contact making it hot and catch smoke).

Must have been a seriously bad contact given the usual current draw of a DVD player. Maybe it even shorted, that could well cause a fire.

I mean I ran a hair dryer on a seriously wobbly adaptor and it didn't even become hot, even though it was awfully close to falling out of the NEMA 5-15 outlet! (if I remember correctly 1200W 120V or maybe even more).
(In case eanyone worries, that was when I was 15, before I joined here).