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That behavior from a laptop is usually caused by a short within the laptop. Taking it to a repair shop or (if still under warranty) contacting the manufacturer about replacement are options. An area on laptops highly prone to that is the power jack itself. You can look up your model Dell and broken power jack repair on your favorite search engine to see what is involved in the repair (some are suprisingly easy - some are not). That may not be where the problem lies but it is common. Does the laptop work with the battery removed? Does the cable feel loose when plugging it into the laptop - or like it can be plugged in more?