Laptop battery from some manufacturers have notoriously short lifespans, and the Ni-MH (Nickel Metal Hydride Battery) which replaced NiCd (Nickel Cadmium) in most applications just aren't that much better. So, you can think about crack open the stone dead laptop battery
back and see if it could be rebuilt. The first thing you'll notice is that laptop battery packs aren't built to be rebuilt, they GLUE the things closed. Took some serious prying to get the thing laptop battery pack open, but definitely in reusable condition.
There isn't a whole lot to a laptop battery, just a hard plastic shell, enough individual cells to make up the required voltage, and a thermocouple. The black wire scotch-taped between two battery cells is the thermocouple, and it's positioned to measure the air temperature in the laptop battery pack, not the actual laptop battery surface temperature. Maybe that's why the batteries fail so fast. The only other component in the laptop battery pack is the little circuit board (below), which has nothing on it but the contacts for the notebook DC circuitry. When you buy a replacement laptop battery, you're just getting a new set of cells to run down.
The individual cells that make up the laptop battery are simply strapped together with little contact strips which are soldered in place. To repair a laptop battery, you need to replace all the cells and resolder. To cost effectively repair a laptop battery, you'd either need to find the replacement cells wholesale, or be doing it for a laptop whose battery is just ridiculously overpriced to start with.