Hi!

So here's the question: what about this battery pack makes the
transformer heat up to the point it burns out? There doesn't seem to
be a short in the battery pack, just a few bad cells. . .I don't
understand why this gives the transformer such grief.

You do have some shorted cells and the charger is doing its best to charge
them up. It overheats as a result...probably because there is no (or very
little) current limiting taking place.

If you were to try charging the cells outside of the pack, you would
probably find that they get at least a little warm and that they don't hold
a charge for any appreciable length of time.

Will using this 24V charger on the 19.2V pack damage the charger or the
battery pack? I understand that this is a really cheap drill, but how
can they in good conscience provide a mismatched charger/pack? Is it
because 24V transformers are so cheap?

Anything is always possible, but there are certain safety exams any
electrical device must (or at least should) pass in almost every country of
the world. Supplying a mismatched charger would probably violate some of the
standards that any of these agencies have published or require by law.

It would be my guess that either the batteries were made to charge at a
higher voltage or that the regulation is done inside the battery pack
itself. I have a cheap spotlight that works this way. The adapter provided
with it is 12 volt, but the battery inside the unit is a 6 volt. There is a
printboard inside that contains the charger plug, a cut-out to keep the lamp
from being turned on while charging, and a large resistor that gets warm
during the charge process.

William