My alarm will also sound if I open the car door when "locked".

I should add that I believe I caused this problem myself. A few days earlier I attempted to lock the car without the keys -- I opened the driver's door and pushed the push button down. It was very difficult to do so (and should have been a warning to me to stop) but it did eventually lock. I have since read in the manual that you should only lock the car this way from inside with the door closed.

I suspect that I bent something by pushing so hard. I'm reluctant to take the door panel off for an exploratory mission so I've made an appointment to have my mechanic take a look. I'll report back with his diagnosis...