Just had a similar situation this morning. The battery is near dead as the key fobs will not unlock the car. However, when I manually open the door, I notice the little stubby lock button doesn't quite make it all the up and out of its hiding position. Normally when I unlock with the fob it the stubby shoots up all of the way.

Well I believe this is what is causing the alarm to shriek as soon as I open the door. The car will not turn over, and the alarm will continue to shriek until I close the driver door. Then the exterior lights flash for a minute or so.

I am noticing some crustations on the battery terminals. Plan on trickle charging the battery this weekend.