On Sat, 23 Nov 2013 07:02:58 -0800, wrote:

In your case, it's very easy to establish if the battery is the
problem or not. Measure the voltage with it connected to the alarm.

The strangest thing happened when I took you up on your suggestion!

A. The battery, connected to the power supply, was 12.87 volts:
http://farm4.staticflickr.com/3785/1...ba3777a7_o.gif

B. I also read 12.87 volts at the very edge of the power supply,
so, the wires are good:
http://farm6.staticflickr.com/5488/1...364f93f1_o.gif

C. I then got 12.87 volts between the battery and the GND spade on
the power supply board:
http://farm8.staticflickr.com/7360/1...cb4a46a6_o.gif

D. But, the strangest thing is there is no voltage between the
battery and the PWR spade of the power supply:
http://farm6.staticflickr.com/5516/1...cf8b97f4_o.gif

I'm not sure what to make of those conflicting results.