Charger center pin snapped and left inside the port

Q:"The charging pin of my laptop charger has snapped off inside the charging port. How do I fix this?"
A:"Get stick that's a little narrower than the power port.
Shape its end to match the shape of the broken-off plug, as much as you can.
Put a reasonable amount of gel-type superglue on the end of the stick, but not enough to spill over the edge when it meets the plug's stub.
Carefully, slip it into the socket so it meets the stub, ensure the rest of the stick outside the socket is supported, and give the glue time to set.
Slowly and carefully, withdraw the stick with its attached chunk of plug.

If it not works, you must replace the jack (and if the plug is also damaged, the adapter will also need to be replaced). On most newer models, the jack is separate from the mainboard and a plug-in replacement

Then buy a new power adapter!

If this doesn't work, try the same but with Blue Tack or epoxy putty, or similar.

(Note: you do this at your own risk. )