The fact that the alarm was chirping three times, but the doors weren't locking mean't that the car was not ready to alarm. It sensed that something was not properly closed, so it would not attempt to lock the doors or arm the alarm. The answer in my case was the micro-switch at the hood that wasn't quite contacting when the hood was shut, but it could have been the micro-switches in the door latches or the trunk. Hope this helps others.
