More than likely the alternator is defective. Drive to your local auto parts store where they will check your charging system for free.
Something is draining the battery. Check all lights. Glove box, trunk, etc. Also check the power window switch.
Perhaps your radiator fan is staying on after the car is turned off. I have recently had this problem, and googled it. And someone else had the same problem.
Yes it did kill my battery
It is on because there is a problem with the charging system. Most likely the alternator is defective.
If a battery light is staying on, it generally means that your alternator isn't charging properly. Be prepared to have to pay for a new alternator, and if it has been damaged, a new battery as well.
Assuming the charging system and battery test okay, you probably have something drawing off the battery when the key is off. Could be as simple as a glove compartment light, engine compartment light or an aftermarket device staying on.
Dead cell in the battery, any light on the car that is staying on, or a stuck relay.
I HAD THE SAME PROBLEM ON MY 1994 VANDEM plas. It was my altenator belt was not tight enough to maintain a full charge. It took me two years to find the problem. It can also be the battery has a dead cell which will drain it overnight. Can also be some light is staying on and pulling power from the battery. Also a stuck relay will drain the battery. Loose or corroded connections is another possibility.
make sure the glove box light isn't staying on There is something drawing down the battery - and a common problem is the door ajar sensors causing the interior lights to stay on. See "Related Questions" below for more about that.
i had the same problem with mine i told a friend about it and he told me to try disconnected the battery for a couple of seconds i reconnected it hey presto it worked.
If just the clock display is remaining on, it's not a problem and is probably deliberate. The LCD of the clock uses so little electrical energy that it is effectively not a drain on the battery AT ALL. Note that LCD watches use a battery that is the size of a dime, and last over a year. The battery in your Saturn stores thousands of times more electrical energy than does the little watch battery. On the other hand... If the radio is staying on, you either have a problem with the keyswitch, or someone has wired the radio to a "hot" connection.
Can be a dead cell in the battery or any light on the vehicle that is staying on. Can also be a relay that is stuck.