Ewww, sorry, its a 50/50 shot, it might be able to be fixed at a reasonable price, it might NOT be cost practical. Really depends on how its attached and what someone would charge to fix it.
Find out the value of the Laptop, at least game it in your own mind, if its worth fixing it or just getting a new one. I.E. check out the price of replacing it, and where the break point to you is, whether to fix the old or just get new.
My daughter's HP had a worn out Charging Port, I was able to get a part off ebay and fix it myself, because the port was seperate from the main board. I'm very mechanically inclined and capable of taking all the little screws and pieces apart and get them together myself, I would NOT recommend it for most people, most laptops are to complex for most people to be able to take apart and put back together. Even for simple things, they are put together so tightly, you often have to take it completely apart to replace the simplest thing on the side.
If that power connector is soldered to the main board, its unlikely you can solder in a new one by hand and NOT damage other things around it, they are usually put together by machines and process's that most people can't fix with a solder iron. And replacing a main board, if you can get one, is often expensive enough to pretty much make a person just look for a new laptop.