The air pump is under the battery area, just as someone else just replied. Sitting directly in front of it is an airpump relay...down there it is just prone to getting smacked, filling with water from the puddle you drove through, etc., etc., etc.

Yes, whenever your battery gets that low, your car is thinking it's being stolen, and with as angry as you are at it, you may wish it was so, but...

Go ahead and jump off the car...so as to not be bombarded with the blare of the alarm for too long, have your wife stand by the door, lock the car with the key, unlock it twice...