Saturn SC2 Won't Start

Alright guys hows it going? Here's the story:

A couple years back (I think 2007) my grandpa purchased my grandma a 1998 Saturn SC2. The car ran great except it would never defrost the windshield, but that's for another time. Well, she died in December 2009 and that past January was about the time she had major issues with the car. One day she tried to start it, and nothing! My grandpa who is a big car guy quickly jumped to the conclusion it was the battery. He replaced the battery and the car ran with no issues for about a month. So then it wouldn't start again and he again assumed it to be the battery. He replaced the battery yet again and this time the car ran for about 2 weeks. Again, purchased another battery and it ran up till a month before my grandmother passed away. So my grandfather just gave up on it. When my family came for her funeral my uncle took a look at it and quickly jumped to the conclusion that it was the alternator!

So he replaced the alternator and it ran for a day. The next day it was totally dead. Now, that was about December 2009 and it sat through a cold and vicious Cleveland winter without starting. Then last summer (2010), my grandfather's neighbor who is a mechanic decided to jump it. Well, he jumped the battery and it started up! My grandpa left the car on the rest of the day to see if it would last. It lasted the rest of the day, but was dead by morning of the next. And since then the car has not been touched, it hasn't been attempted to start or anything since then.

So my question is what could possibly be wrong with it? What could I do to fix it? What went bad? I really appreciate anyone who answers, it'd just be so relieving to get it running again.

There's a draw on the battery after keying off.

[Not so] Simply a matter of tracking it down.

Many possibilities from a bad ignition, to a stuck relay(s), to something plugged into the outlet/cigarette-lighter.

Start with a charged battery. Remove the key from the ignition. Get a volt meter that has amp-draw measuring capability. Connect the amp meter in series with the battery positive terminal. Note the amount of power being draw. (some draw is normal) DO NOT ATTEMPT TO CRANK IT WHILE THE METER IS CONNECTED. Jiggle the ignition around to see whether the draw reduces. Individually pull and replace fuses until the draw ceases.

Using a circuit diagram, and knowing which circuit(s) is/are responsible for producing the most draw, you can begin to track down the componenent(s) that is/are responsible.

Let us know what you find....