I've seen a few references to laptops sounding warning beeps when the battery runs low but not desktops/Cmos battery.
When you say "even when everything is turned off" do you mean the mains lead is disconnected?
If so then the Cmos battery is the only source of power and it sounds like a motherboard function.
Check your motherboard manual or the manufacturers website to verify this.
If you still suspect the CMOS battery, changing it is cheap and easy but you should note your BIOS settings before you do. There a few freeware programs that will do this for you. Obviously save the results to floppy and print.