Alarm going off randomly w/out cause

Hey, y'all This is related to my 05 GT

So here's the problem, last week my wife was driving the car and went to turn the alarm off in the pkg lot at the grocery store, when she opened the door the alarm went off, but she had heard the doors unlock, and the door was unlocked when she opened it. She finally put the key in the ignition and turned the car on, which turned off the alarm. As soon as she turned the key off, the alarm (horn) sounded again. She eventually got it turned off by actually starting the car.

Later that night the alarm went off in the driveway for no reason. It deactivated w/ the key fob. That was 4 days ago. Last night it did the same thing. It would not deactivate with the fob, but it did deactivate when I turned on the ignition. This happened at midnight, so needless to say my neighbors are not amused. I have disconnected the battery (neg) so it should not go off again. Also, if this makes any difference, the cable between the E-brake handle and the block for the rear cables broke, so I leave it in gear w/out the e-brake pulled. I'm waiting for the parts.

I know this is long but I appreciate your input

Thanks

Pat