The people who make laptop (and desktop) motherboards apparently don't know what a thermal relief is. Those power connectors and other components on motherboards are soldered directly into giant power planes. Basically, it's like trying to solder to (or desolder from) a giant heatsink. Doesn't really matter how powerful your iron is (and no way 25/30W is enough), you simply can't dump heat into the joint fast enough to melt the solder.
What you need to do is basically bring that section of the board up to reflow temperature. I just use a plain ol' heat gun for this. Yes, like one would use to strip paint. I have one of the fancy adjustable temp ones from Wagner Spray Tech, but a normal one will work. Just use the "low" setting. It'll get plenty hot. Wave it around over that area of the board until it gets hot enough for the solder to be molten, then lift the jack off using needle nose pliers. Be very careful when you do this. It will take about a minute or so to get that section of the PCB hot enough, and then you need to act quickly. You don't want to start a fire, and if you bump things around too much, you'll also cause parts to move around or fall off the board (remember, the whole area is molten).
If you'd rather not do this, then you can try using several reasonably high power, temperature controlled irons. You'll need one on each section of the jack that's soldered down. There's no way you'll be able to wick enough solder off of there to just remove the jack. You have to get the whole thing to reflow at once. I've never had much like with this method. The only real method I've found that works is the heat gun. The heat gun works pretty reliably, but you've got to get the hang of it, so try it out first one some scrap boards or similar (real FR-4, not that crap phenolic FR-2 crap they use in TVs and monitors).