Stynus saw the Drill Battery Charger Repair article and sent in his drill repair to Make a Cordless Drill with a Dead Battery a Corded Drill. In his case he had a battery for his Bosch cordless drill die and with the cost of a replacement being so high he decided to adapt the drill into a corded drill for bench work. He still has the ability to use it as a cordless drill since he still has one functional battery pack. Even if your battery charger is still good the current output from the charger will not be great enough to power the drill.
By gutting the battery pack of the old nicad cells and installing a connector directly to the internal power connection you now have a simple way of powering the drill using an external source. Stynus is using his 12 volt bench supply to power the 14.4V drill so it won’t have the same power and speed as the battery pack did but it will still be usable. A simple series diode protects the power supply from reverse EMF that would be caused by the motor.
One other thing that can be done is rebuild your drill battery pack, you can often get replacement nicad cells quite inexpensively compared to the replacement battery unit from the manufacturer.