Before changing the battery on the DSC832 (PC5010), the keypads and motion sensors were all lit. They went dark as soon as the old--and very weak--battery was disconnected. After the new fully charged battery was connected, no power returned to the system--the keypads and motion sensors remain dark. How should this be troubleshot? Unfortunately, the main current breaker switch was not turned off before the old battery was removed; but neither was it tripped afterwards and the transformer is still getting power.

Try turning off power to the receptacle that powers the transformer, Disconnect battery and reconnect, Verify Battery Polarity was/is connected correctly. Reconnect AC power to transformer.
If still blank, verify AC is Present to AC input terminals.
You WILL get a Trouble light, telling you to reset the clock.
*2 shows troubles.

Thank you, Stratmando. I'll try that.