At this point it would be good to mention you should really discharge the pack before you continue. Don't play with electricity unless you know what you are doing!
Step 1: Let's find out what is inside!
Fortunately for me the internals were looking familiar, a simple set of "Sub C" rechargable NiCd cells from my RC car racing days. I used to build my own racing battery packs so I couldn't help applying that here.
I had visions of using batteries that power world championship RC cars and transform my moderately powered B&D into a drill that would make screws and yet-to-be-drilled holes tremble with unspeakable fear.
When you open the battery you'll need to save some plastic bits detailed below. Don't break them.
Step 2: Replacement Sub C Cells
These fellas cost me $1.79 each for a grand total of $21.48 from Budget Batteries. So far so good.
In case you aren't good at math, a 14.4 battery takes 12 1.2V cells to make up a pack.