Reddit reviews Hakko 472D-01 Digital Desoldering Station with Built-In Vacuum Pump, Pencil Handpiece, 24V AC, 110W
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Pencil-style desoldering toolDigital temperature displayZero crossover switchingESD-safe by design24 in. Hg Vacuum pressure and 15 L/min suction flow
You can get any laptop jack at http://laptopjacks.com. Tad pricey, but you are guaranteed a new part that fits your machine. You won't be able to salvage yours I'm afraid.
You really need a solder sucker to suck out the solder. They have manual tools for this like this or versions that are just a soldering iron hooked up to air suction, though these are kind of expensive. Portable, Station
The problem is several of the legs on the jack are grounds and thus connected to all the grounds throughout the board. Sometimes it is hard to get them hot enough, I've had to use two soldering irons, one on top and one on bottom just to get all the solder to melt enough to suck it out.
My recommendation is find an electronics shop and have them do it for you, you don't want to tear the copper out of the circuit board or you'll then have to run a jumper wire. In my shop if you brought us the laptop motherboard already disassembled and the jack we would only charge a half hour of labor. (This is assuming the board hasn't been damaged)