Our laptop has melted its DC power lead plug due to overheating.

Depending on the age, you may be able to argue that it has failed within
what would be considered a normal lifespan for the goods and get it
repaired free. As a UK consumer IIRC, the vendor may be responsible for
the durability of the goods for up to 6 years, but will usually try to
hide behind the "out of warranty" mantra to avoid having to do anything.
The initial cost may also have a bearing on the odds of getting a free
repair too...

How old is it ?

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