Both batteries dead.

AC to DC adaptor purchased for project.

Female coaxial part.

Match the voltage of your drill to the voltage of your adaptor.

Get an adaptor with 5 or more amps to increase the torque on your drill.

Open the battery pack.

Look inside. I was surprised to find a circuit board attached to the cells. I incorporated it into the fix, not knowing what it does.

Understand the polarity of your adaptor.

Understand the polarity of your drill.

Understand the polarity of your drill.

Understand the polarity of the female part. Solder wires on.

Solder the correct wires to the correct polarity connections left from the removed battery cells.

Drill a hole and install the female part into the housing of the battery pack.

Recycle your battery cells at any home improvement store.