I think you need to figure out why your laptop fried. This will be really difficult if you are not an electrical engineer with the schematics of the board. Your PSU could be bad, you could have shorted/damaged something on the motherboard, or any number of other options.
Of course, you could try flowing more solder into those holes and putting the jack back in place, but that won't solve the reason your stuff "fried". Same thing with buying a new jack and soldering it on, you still don't know what caused the problem.
IF it is a damaged jack, that MIGHT be the reason. It looks like it fried around the 19v (or whatever it is) plain, like there was too little solder from the factory, but it's hard to tell at this point. You can try putting it all back together and seeing if you don't mind buying a new board/psu if it fails.