How the System Works
A smoke detector isn't really a smoke detector, a smoke detector detects particles in the air and calls the particles smoke. Too much moisture landing inside the detector can also cause it to go into alarm. At this point, most smoke detectors also turn on a red light to show you where the alarm is coming from.
The alarm company only monitors the alarm system in the home. When there is a fire or burglary alarm, the security system picks up the telephone and calls the alarm company to say "Fire" or "Burglary". Then the system hangs up the telephone.
The alarm company then calls you, not your fire/burglary system, to verify that you are OK. They talk to you, but they have no capability of doing anything with your fire/burglary system at all, you have to reset the system yourself.
Normally, blowing the smoke or steam out of the smoke detector, and then resetting the system will put the fire/burglary system back to normal, ready to detect alarms again. (Usually resetting the system requires the normal arm/disarm password for the burglar alarms system.) When the system, which includes the smoke detector, doesn't reset with the normal way of resetting, there is trouble with the system.
If you aren't tech savvy, or if you feel at all uncomfortable working on the system, get a professional company in there to check out the system and service the system. Doing so right away can save you lots of headaches later.
You did power the system down, and disconnect the batteries, but the batteries alone are a potential for big problems. Make sure to reinstall the batteries the way they were before removing them, or the whole panel in the basement may have to be replaced.
When you do any further work on the fire/burglary system, call the alarm company to make sure they don't send the fire trucks or police. Professional service people make that phone call, you need to make that phone call.
What you did when you disconnected AC and the battery was to "power-down reset" the system. A power-down reset is the same as turning off and on your computer. The whole fire/burglary alarm system including the smoke detectors should have been reset when the system was turned on again. Unless something was already bad and needed replacement, doing that kind of reset should not cause a problem.
However, the system did not reset when you did a power-down reset to the system.
Smoke Detector Still in Alarm
Is the red light still lit on the smoke detector itself? Is there a yellow light lit on the control panel? In either case, the smoke detector did not reset properly. The major cause of this kind of problem is showing that the smoke detector is bad.
Having a bad smoke detector sometimes happens, and the way to fix a bad smoke detector is to replace it. Extreme care must be taken to make sure the new smoke detector is EXACTLY the same make and model as the old smoke detector, and also extreme care must be taken to make sure all wires land on the new detector EXACTLY the same way on the new detector as old detector was wired.
Any mistakes while replacing the detector are hard to find and repair, so getting a professional company in there to check the fire/burglary system out might be the best idea.