I had a similar problem when I first bought my accord. I was outside sprouts and suddenly my alarm just goes off....and despite everything I try to do, I can't get it silenced. It would go off randomly and go on again. If I tried to open the door (with it unlocked) it would go off. It was crazy. It ended up being the alarm system. The car had an after market system that was probably really old and on it's last leg. Replaced the entire alarm system and never had a problem. Check out your local sound/alarm guy and get a new reputable system.
Watch my Youtube video for a better understanding its up there in the first posts, except mine was just a silent alarm, when i did get the car i think it had a somewhataftermarket system and i ripped out the horn it had from the engine bay, after all it worked on its OEM alarm system thats about it