This answer is only applicable for soldering and desoldering PTH components used in modern multilayer(4-12) PCB.
Laptop and desktop motherboard manufacturers are continuing use of Lead Free Solder(LFS) for last 5-6 years. This kind of solders' melting point starts at 217 degree Centigrade(C). There are different kind of alloy composition used in manufacturing LFS, whose melting point differs. But only 217C - 227C LFS alloy used in motherboard manufacturing because of its lowest melting point in its class.
Now, it is not the matter of the solder used in your motherboard is leaded (63/37 at 183C) or lead free. If you use a traditional soldering iron / station, you will not be able to melt the solder on the power jack of a motherboard. Only because the motherboard is multilayer and has a wide ground / positive supply copper plate. This wider plate absorbs the energy from your soldering iron, and drops the tip temperature (drop may be between 70C - 100C than your set temp) within seconds. For tradition soldering station even with microprocessor controlled, it is near about impossible to rise and maintain the temperature immediately, because of the heater and sensor accuracy.
The watt and the temperature mentioned in your soldering station will not help in this matter. Rising the temperature will probably damage the solder pad on the board and will not melt the solder on the other side of the board.
To work on modern motherboard, it is necessary to have latest soldering station from any reputed brand, whose temperature rises to 350C within 5 seconds and minimum temperature drop (30C - 50C). Always set your soldering station temperature minimum (solder melting temp + 70C) and increase if required as per application. Using of proper size iron TIP is necessary. Before soldering motherboard it is necessary to clean the iron tip with a damped sponge(made with cellulose) and brass wool / inox wool.
Before desoldering the PTH components, it is necessary to clean the terminals with isopropyl alcohol. After this process, add some new solder to the terminals of the component to be desoldered.
It could be that the joint is covered in some particularly strong conformal coating that is actually solder-proof. Some time ago, I was trying to unsolder wires form a computer microphone and I used 80 W soldering iron at 400 C for maybe 30 minutes on the joint and I still couldn't remove the solder. I tried sanding the stuff away, but I couldn't even scratch it. I think that they ought to paint tanks with that stuff. :) – AndrejaKo – 2012-01-14T01:03:59.183
A laptop of any recent vintage will have been manufactured with lead-free solder (it's been the standard for a number of years now). If your iron isn't specifically rated for lead-free, it's probably just not getting hot enough. You probably need to invest in a new iron. – Michael Kohne – 2012-01-14T01:05:42.457
@Michael Kohne From where did you get the idea that some special irons are needed for lead-free soldering? – AndrejaKo – 2012-01-14T02:28:50.497
Common lead 60/40 solder melts at 190C. Some lead-free, high-strength solders require as much as 485C to melt. Though I'd be quite surprised to find anything requiring over 300C on a part made with so much plastic. (The ultra-high-temp solders are usually used only on ceramic substrates.) – David Schwartz – 2012-01-14T02:40:41.750
@AndrejaKo - Lead-free solders melt at higher temps than leaded solders. Older single-temp irons were calibrated for a proper melting point for standard leaded solder, and won't touch the lead-free stuff. Further, older variable temp soldering stations don't always go up high enough to deal effectively with lead-free solder. – Michael Kohne – 2012-01-14T02:47:38.790
Add to that , The boards now are huge heat syncs. the wattage of the soldering gun is one thing. The rate that the Tip Cools at is the other. When dealing with the heat being rapidly removed via any forms of heat spreading or heat syncing, keeping the soldering gun on it is just going to make a mess. Having a nice copper core pencil/gun with a good conducting tip, and making sure it is heated and doesnt go cold on touch. I have been in heat synced situations where a Weller at 240W and its small tip did not work, and a good pencil with large core would work instantly. – Psycogeek – 2012-01-14T06:43:32.833