How can I test my drill and batteries for faults?
Testing batteries with a multimeter

Charge the batteries for a bit (follow the manufacturers instructions for the recommended charge time).
Set your multimeter to a low DC voltage setting.
Touch the black probe to the negative terminal on the battery, and the red probe to the positive terminal.

If the reading on the multimeter is at or above the voltage listed, the battery is good.  Otherwise, you'll want to replace the battery (Don't forget, many home improvement stores offer battery recycling).