Door lock/alarm problems on 2000 Cougar

Hello everyone. I have a 2000 Cougar. The alarm system has suddenly decided
to stop working. The batteries in the keychain thing-a-ma-jiggies are new.
The red lights that's on the dash (which usually blinks off & on again) is
now staying on all the time. Although if you look at it closely, you can
tell that it's still "pulsing" as the red light goes from dim to bright and
back to dim again at the same pulse that it normally flashed at. Also, the
auto door lock feature has stopped working. Press the lock or unlock button
and nothing happens. However, you can manually lock the drivers door and
that will automatically lock the passenger's door. It's almost as if the
alarm is stuck in limbo between on and off. Other than these symptoms, the
alarm/door locks don't give me any problems. The car starts, drives and
shuts off normally.

Anyone had this problem before? Any thoughts on what might be the problem?

Sean