2004 RAV 4, lights on alarm doesn't work

I have the 2004 RAV4. My car does not beep like it used to when I open the door and have left the lights on. I have run down my battery so many times -- AAA now charges me extra. Also, if I open the door with the keys still in the ignition, I don't get a beep on that either. Battery is good (now new), alternator is good and fuses are good. What could it be?

I don't know if it's related but my factory key alarm locks the doors sometimes when I haven't pressed the button.