This might not apply in your case, but I had a similar problem on an old Impala of mine. The battery was weak or getting drained somehow, and when it's voltage got low enough just sitting there, the alarm would automatically reset itself, and when it did, it would go off. Sounds like yours is going off like this, and you mentioned that the car won't start when you do. If that's because it won't even turn over, then perhaps the battery has something to do with it.