Thanks Klaus and Ozark Lee. The alarm has been disabled, and now I can also diagnose it, if it needs that.

I'm starting to think the alarm is a symptom, not the problem.

To recap, my 5 year old battery went flat after a couple of days, and cranking had been getting weak anyway, so I replaced the battery. A few days later, my wife kept hearing a car alarm going off, only to find out it was the 850. Nothing was wrong, hood was closed, doors, trunk, etc. Leaving the car unlocked did not stop the alarm from going off. So I disabled it per Ozark's post.

Well, the battery is still going dead, so obviously something else is wrong, and that will be this afternoon's job. The glove box light has been removed, and the trunk light unplugged, yet the battery still goes flat in a couple of days. So I guess I'll put an ammeter in the circuit and start pulling fuses until I find the offending circuit and go from there.

Here's another question on this: On old cars with mechanical voltage regulators, the contacts could get stuck and drain a battery. I don't suppose there could be a similar problem with electronic regulators could there? How about a bad diode in the alternator? Could that drain a battery with the car off? (The car charges fine, though I've not tested voltage yet)