Last night I had to have my car towed because it woudl not start. Iwas able to push start it however it would not idle. The lights were very dim and if I tried to push the gas it would die. So today I got the car home and jumped it. It jumped fine and was idling very well. Once I tried to drive off however the car died. Wouldn't the car not idle if the alternator was bad? In order to start the car it must be jumped again.