I read a thread somewhere on the NAM forum, about 3 years ago, regarding the factory alarm suddenly stopped beeping when the door lock/alarm was activated.
Can't find the thread. Anyway.....

I have an 04 MCS R53. with a factory installed alarm.
About 4 years ago I moved from a year round, sunny and warm climate whereas the temp rarely ever dropped below 35° during the winter months
Since moving to a state with more of a "seasonal" climate, my alarm went off at random whenever the temp dropped below 40° - 29° = lights flashing, alarm screeching. ' Really annoying @ 3am.
Until the siren finally stopped working. Only lights would flash. The alarm siren hadn't worked since.
I like the alarm siren.
I've been doing a significant amount of repairs to my Mini lately R&R(ing) with new parts. I finally decided to look into the siren alarm. Replacement part = $150 -$200...for something that makes noise.
So, I removed and took my old one apart. Thinking that I may have been a little rough pulling the two halves apart - I discovered a detached negative wire underneath the breadboard. Soldered it back in to place (thinking it couldn't be that simple of a fix) and installed it back in the car.
What do you know? - It works!

Times are crazy these days with all the senseless crime. Car break in/thefts in my area have gone up 35%.
The alarm may not scare off a thief...
I just want my Mini back to the perfect way it was.

Edit:
FYI - I neglected to photograph the procedural fix because I never expected it to work. Siren Alarm designs and pinouts vary from year to year; Below, I've uploaded images of siren alarm that matches my '04 MCS
(I purchased this one from Ebay before I managed the fix to my original )...