Define shut down? Does the car crank when you turn the key? Does it just click? How many miles are on the car? Any recent reapair history? Is/was the CEL on? How did the car run before it died? ie..idle, performance etc etc...What do you mean back lights? brake lights? turn signals? reverse lights? just reg lights like the headlights are on? A shot from the hip here is that someone left/accidently hit the virgin switch on ontop of the steering column. This switch will keep your parking lights on even when the key is out of the ignition, thus draining your battery if left unattended for a long period..from the information you have provided I would check that switch first..