Without being able to look at the machine and tinker with it and the power adapter in-person, it's hard to tell. [br]
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That said, based on what you wrote I would suspect either the battery or the power adapter failing, if I had to guess. [br]
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I'd personally try a new power adapter (being careful to keep the packaging safe for potential need to return it) to see if that resolves. If it doesn't, I'd personally guess the battery was dead and needed replacing. [br]
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There's no swelling in the case along the bottom, especially where the battery is located, correct?