well typically when your driving and your car starts to die , it would indicate a bad alternator, because the entire car runs off it and takes over once the battery originally starts the car. however ive heard of instances when the battery going dead causes problems in the entire charging system once driving.
what light is on when the car is tried to start? is it the battery light? or a check engine?
if its the battery light then that would be the alternator , that light is telling you that there is a fault in the charging system (alternator) *-note that the abs light will usually on as well because it automatically shuts off when the sensor notices a problem in the charging system.
what i suggest is that you get a volt meter and battery charger , charge the battery, start the car and see what the volt meter reads, if its reading 12.9-14ish then its probably your battery, if its above 14.9 or below 11.0 then you have an alternator problem.
um i cant think of much more, but if you have questions ask them i might remember more. im just tired today and even though i did my own trouble shooting and removed and replaced my alternator , im still a little sketchy on details. ( so if i aint clear on what ive said then ask me again