Well, one "wire" will be in the form of a layer of conductor surrounding a single wire - This mesh will be the negative connection, the positive connection will be the single wire in the middle. you have to pull the mesh out in order to connect it, you gotta do this to both halves of the broken wire, so in fact you may have had the polarity correct but simply didn't have both connected.
I've fixed many cables like this, the problem is, the end which goes into the laptop is molded, so you can't just get a new end.
I suggest getting a multi-laptop adapter, they usually have all of the connections needed and you set the voltage on the transformer. Some of them figure out the voltage automatically, but those kind break easily.