This may work on your cars...it does on mine which is a pre-'96 factory alarm:
Pull your alarm out from behind the dash (it's a bit of a challenge to get to, but there's a FAQ on it in this forum). There are switches on the alarm to turn on/off the chirp and other options. I'm guessing that when you lost power, the electronics defaulted to chirp-off.
<span style='color:green'>1994 325i </span>- - - 75,000 mi.
No mods - - - very happy as is!
<span style='color:green'>1995 525i </span>- - - 154,000 mi.
No squeaks or rattles... unreal!