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so long as i can get the part i can do it, hot air soldering is great for getting multi pin sockets off without damaging the board :)
maplins do standard ones for a couple of quid, even if it was a dry joint i would replace the socket to be on the safe side, and with it being low power over the pins its not hard to reroute any burnt out holes on the board, so yes it can be fixed, and no it wont cost a fortune.
plus the lappy gets a mini refurb as its a full strip and rebuild.
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If its a fairly newish Laptop and the damage isnt that much, if its only the power connector then you should be able to get it repaired quite easily...
However if its a pretty old laptop (2 years +) i find that some repairs as simple as they perhaps might be can cost more than the laptop is worth..