One more vote for a simple solder station. You'll drop just under $100, but in my opinion this is the RIGHT answer.
If you are working on circuit boards....assuming that this is where the laptop power connectors are connected...then you really should be using a temperature controlled iron.
And if you've never used a station, it is hard to explain the difference. But, it makes soldering EASY and consistent. Those simple fixed wattage irons simple deliver the same power all the time. Let them sit too little before using and they are cool; let them sit too long and they start off way too hot.
Either the Hakko FX-888D or Weller WES51 would be a fine choice. We've got both at work. I like the WES51 for very small stuff but that could also be a factor of having the smaller tip on it most of the time. The Hakko wand is a little bigger around and just 'feels' better to me. And I believe the Hakko is a little more powerful, so it can deliver more heat when working on bigger connectors/junctions...check the spec sheet as I am making the more power claim from memory. I ended up buying the Hakko for my own at home.
I typically use the chisel tip that comes stock on the Hakko or just one size smaller.
I would also recommend some 63/37 solder. This will change states between liquid and solid quickly so let chance for errors if parts move while cooling.
I noticed there is a deal on Amazon now where you can pick up the iron along with a free pair of flush cutters for a good price.http://www.amazon.com/Digital-FX888D-CH ... rds=CHP170
Final thoughts. I've never been disappointed when I've invested in a nice tool. But have been frustrated when I've tried to go on the cheap and got a bad or wrong tool for the job.