There's obviously an electrical drain on the system somewhere....this can be down to courtesy lights left on or similar etc, but its possible for an alternator to also run the battery down due to a diode pack problem. Likewise even a new battery if faulty can internally discharge. So - to check the battery, remove the terminals once its charged, leave it for a while, reconnect and see if its still charged. Likewise the alternator - disconnect the leads overnight. If the car starts up in the morning, it could be the problem.
John, April 2009
