You open the puppy up, remove the mother board and de-solder the jack and then solder the new one in place... (yes you can find and buy a replacement on line an example here), shop around, Sounds overwhelming perhaps, but here is a video of a fellow doing this. Note, you don't have to have the expensive hot-air tool he uses to solder and de-solder, it's nice, but not required. By the way, check that the plug on the end of your power cable isn't the problem first... they sometimes break too and are an easier fix.
Good Luck
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