It depends on if its a model they sold at best buy at any point. They dont replace screens in store though it would need to be sent out to the best buy hardware repair center. Honestly if the laptop is old its usually not worth repairing due to cost. You could always hook it up to a monitor and continue to use it.
If not you might want to check a shop in the mall. I can't remember the name of it but they have a sign in the window that they can do screen replacements for pretty much anything. Also you can try staples, they offer repair services, just not sure if it extends to laptops.
They should. I would call them before you bring it in
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