"Disclaimer: I've made these instructions only for people experienced with soldering and repairing computers. If you don’t feel comfortable doing this job, please do not open the laptop or you can permanently damage your computer. Take your laptop to a professional repair shop instead."
"For this repair you’ll need the following tools."
I’m going to solder the power jack from the motherboard, clean contacts on both power jack and motherboard and then solder it back in place – this is the proper way fixing the power problem.
Be careful. Inside the positive hole there is a copper sleeve which connects the terminal on one side of the motherboard with the traces on the other side. If you are removing the power jack with force, you can pull the sleeve from the hole. You don’t want to do that.
UPDATE: If you accidentally removed the internal sleeve, check out this post: How to fortify damaged power jack connection.
So, do not apply any force and make sure the solder is melted when you are removing the power jack. I hope you understand what I’m talking about.