2001 Silver Sport Rx 300 Electronic Alarm System

[Silver Sport]

We are having a problem with the alarm system in our 2001 RX 300 Silver Sport. The alarm goes off if after you get out of the car and shut the door without locking the door, or if you just lock the door and walk away it goes off. But if you hit the unlock button and then the lock button it wont go off. Clear as mud huh? Anyhow, we were wondering if this could this be related to the key FOB being partially broken.

We really like our Silver Sport, but this is becoming embarrassing with our neighbors. Any thoughts would be greatly appreciated.