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power cord small pin loose; replacement of power cord did not correct

if you mean the pin in the socket of the actual laptop then a new charger wont fix it, it will probably need a new charge port

Take off the back cover by removing the small Philips screws and gently pry off the back. Check the power connector, there are plastic tabs that hold it tight to the side of the case. They break easy so you need to tape it down with electrical tape or glue it in place.

The port is going to be loose, if you look at the port internally. It is not actually attached to anything inside and is held in by a clip, this is what causes it to be wobbly