I would tend to agree with both of you that if the lights aren't flashing it would seem to be an alarm malfuntion issues and not the Bcm.
Mine was Bcm related and I had the lights flashing.
Did you resolve your window role up issues with flashing the Bcm?
I would just suggest that if you are to take everything apart under your hood to disconect the alarm module you may as well just get a new one now and put it in while you open it all up as opposed to doing the work twice to remove everything.

Also while you have all that apart you may as well do the wiper arm rubber grommet modification while you have access to removing the cowling.
There are many threads showing exactly how it is done to repair this manufacturing defect which left the driver side wiper arm without a rubber grommet since the factory hole was misplaced... Just a thought.. Assuming that your car hasn't already corrected in that manner by yourself or previous owners if there were any.