Wow- A smoke detector that could cause a fire..
It is very difficult to say
It could be a fault in the fire alarm- short circuit that caused the battery to heat up to a cooking point.
It could be a chemical fault in the battery where atmospheric pressure and chemical imbalances caused by some impurity during production caused the battery to heat up at a certain point of its life.
Either way
The safest option is to replace both and remove all doubt!
eg ever hear about the exploding iPods... :)
The system is designed to dial out on a phone line to a central station or a police monitoring system. These alarms have built in warnings for a failure in the phone line. This is a safeguard so you know the system is not working properly.
So long as the system is operational and cut off from the phone line, it will continue to beep. By removing parts of the keypad and circuit board, you have apparently shut down at least part of the system. If you truly don't want the system on, you need to remove power from the entire system.
The power to the system is probably controlled by master box (probably where the battery was) that has a wire running to a transformer on or near your main power panel. The simplest way to stop the system is to disconnect the wires going from the transformer to the alarm control panel.
The transformer wires are low voltage (usually 24 volts) on the outside (inside the panel they are 120 volts). To be safe, it is better to turn off the breaker connected to the transformer before disconnecting the wire. If you cant figure out which it is, have a flashlight handy, turn off the main breaker, then disconnect the wires. Then turn the main back on.
Once the system is disconnected form both the mains and the battery, it cannot send a false alarm or activate the safety beeper.
Best Answer
I was wondering the same thing and noticed there is a little latch under the text "slide to remove" which had to be lifted (with a screwdriver) to get the unit out from the ceiling. At least in Finnish version there was a text "lift the latch to slide unit off" which I noticed when I took a picture below the lid.
I know it's an ancient post but I thought this might help someone! :)