Brake pedal draws power stalls car

... the ammeter pegs out to zero ...
Great responses. I'll just add that if your ammeter is normally showing "C" or "D", something is wrong. It should only go to charge for a short time after starting, while the battery is re-charging. It might show slight discharge at idle w/ full load (headlights, brake lights, stereo, for sure if a radiator elec fan). Otherwise, it should stay about zero, so if not something is wrong, but probably unrelated to your main issue unless it indicates a constant short to ground that gets worse when you push the brake pedal.