i know it sounds silly but if the batt light stayed on before the car went dead ya have cheacked the belt is still on the car

as when they snap or the alt gets fried ( as in jumpstart with leads on back to front) thew bat light stays on

also did the rev counte start dancing with the music to as thats another sign

if the alt aint charging enough it will appear very very dim when all the stereo, lights, heater is on then finally ya loose the lot, the car will start again after 5 mins though then go dead again