Morse code.

If you don't know it, you have enough time to learn it before the batteries
go dead :)  Seriously, a beep code according to some scheme you make up, or
use some digital code and build a decoder for it, if you need something to
occupy your time.  Presumably you can hear the beeps in the house, so the
hardest part (remote signaling) is solved.

A PIC could do this.  Sample the alarm, and if it's acting like the
battery's dead, have the PIC able to sound the beeper itself.  Then you make
up your secret code.   Either use a micropower PIC, or make a circuit that
lets the PIC shut itself off, and have the alarm kick it back to life.
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