Chosen Solution
I have a very old compact drill that has served me very well. But it’s died. I would like to fix it. I have recharged both batteries and swapped them out: nothing. It was working ok then just stopped - no sign of anything going wrong beforehand. Where do I start with identifying what’s wrong? Any suggestions as to most likely causes of the problem?
The above answer is assuming the batteries are actually good, which is the first potential cause. They may appear charged but have such high internal resistance that you can’t get enough current out of them. Try testing them with a resistance load and a multimeter.