For Anyone Who Knows Anything About Cars.... I Need Help

So my new car (3 weeks) is having a problem. It's a 97 Mits. 3000gt SL. And I love it... save this one thing that just started a few days ago.

It runs absolutely fine when it's started, but the issue is with the battery or something.

When it sits over night, the battery is dead the next morning. Dead as the grave- not even the clicking sound or dim lights. I can jump it off, let it run, and it will be fine all day. Once that battery is charged I can turn it off and start it back up a couple hours later and the power's fine. But over the night, the power dies completely. 

I've taken it to two different autozones, they've tested the battery and alternator and say they're fine. Nobody can figure this out. Any ideas? I really need my car to run tomorrow.

When was the last time the battery was changed Led_poison

could be that, possibly wiring, heck even possible ignition malfunction