Once again I came home to find my laptop power cord with teeth marks near the end and it crackling with electricity every time I moved it. It seems that my mother's cat just loves to chew on this thing leaving me without a way to charge my laptop. This is the second time I've repaired it, so I figured I'd make an Instructable to help any other poor souls with a cord loving cat.
WARNING! You are dealing with a power adapter which can cause fires if wires get crossed in the process. Please use caution, make sure the cord is unplugged before starting, and don't blame me if it doesn't work.
Step 1: Cut Out the Badness
This whole process should only take about 10 minutes or so. Begin with plugging in your soldering iron and unplugging the laptop power adapter. Start looking at the cord and see if you can find the problem section, in my case it was pretty obvious (See picture). Then take a pair of scissors or a cutting tool such as tin snips and cut out the problem section. You will want to cut as close to the problem as you can so that you don't lose too much cord length.
Step 2: Begin Stripping
So now you should have two cut pieces of your power cord. Slide a piece of heat shrink tubing down onto one of the pieces of wire and move it out of the way for later on. Take a wire stripping tool or a pair of scissors and begin peeling back the insulation from the wires. Be very careful not to cut too deep as you'll have to cut the cord down again. If this is your first time stripping wires I would even recommend practicing on a cheap extension cord you don't mind loosing. As you get through each layer, twist the inner wires together in order to keep them all together. In my case I had two outer layers and then a center wire.
Step 3: Add Some Heat
So now you should have both sides stripped and the individual strands twisted together. Take the center wire from both sides and twist them both together. Then add a bit of solder with the now hot soldering iron (It should still be plugged in from step 1), and tape off the wires with electrical tape once it cools. Make sure that the inner most wire is completely covered with electrical tape or it could short circuit and start a fire! Do the same thing for each layer working your way up to the outer most layer. I've found that alternating sides that you connect the wires up on helps to keep the cord looking a bit straighter.
Step 4: Finally!
Leave your last connection without any electrical tape on it to make sure everything works. You may want to carefully test your adapter now in order to make sure that all the connections are secure. Plug the adapter into a surge strip and keep your hand on the power switch to make sure you can kill power quickly. If everything works, move the heat shrink tubing up over the connection and use your soldering iron or a hair dryer to shrink it up. Keep moving the heat source so that the tubing doesn't melt apart. You have hopefully successfully repaired your laptop power cord for now. Hopefully the cat won't eat it too many more times!