Pete (above) is spot-on.
You are better off buying a new drill: Lithium cells (3.6V) are a much higher voltage than NiCd (1.2V). You need fewer of them and you need a very different design of charger. But...
... If you carefully dismantle your old NiCd battery, you could turn it into a car or motorcycle battery adaptor:
Keep the case, and carefully wire some thick* power cable to the main connectors inside it, and out through a hole in the side** of the (empty) battery case, to "alligator" clips for the car battery.
Recharge the replacement battery with a car/motorcycle charger, NOT the one that came with the drill (car batteries need different charging from NiCds). There are usually extra, small connectors on the battery. These are for a temperature sensor, only used when charging the NiCds - you can ignore them. If the drill has a battery charge indicator, this will not be accurate any more.
Make sure you get the + and - connections the right way round (label your alligators too!). The motor does not care (it will just run in reverse), but if the drill also has electronic speed control, that might be damaged by reversing + and - .
I know this is not as convenient as cordless, but it will work, and if you have an old (not dead!) car battery, it's a good use for it. It also only costs you some alligator clips and cable (if you already have a battery). Please recycle the NiCd cells inside the battery if you can - the chemistry is very poisonous for the environment, so do not just throw them into landfill.
The thicker the cable you use, the longer it can be. Thinner cable will steal some power from the drill, and you will notice the difference. Car batteries need to be kept charged though, so you can't work until the battery goes flat, as it will be damaged.
Then you have a new drill (that you have bought), and a useful spare.
* Lots of copper -- HiFi or PA loudspeaker cable would work, too, but may not be robust enough for site work!
** This is so it will still stand when you are not using it. You might need to put a heavy weight in the bottom of the old battery case too, so that it doesn't tip over. If you use a metal weight, make sure it cannot touch the connectors inside.
