Replacing the lower case is something you could do. Here's the IFIXIT guide: [guide|337] its a fair amount of work but something one could do them selves.
As for Apple fixing it sorry to tell you they no longer service this series (Apple Store) some authorized service centers will still work on them as well as independent repair shops.
I would first try replacing the Left I/O board which is where the MagSafe connector is located. Here's the IFIXIT guide to get to it: [guide|333]