My DSC alarm system keeps beeping and saying to replace the battery. The only battery I can find is in the basement where the box is with all of the wires. It's a big black battery. Is this the battery I am supposed to be replacing?

It may be telling you to replace a wireless device battery,
What happens when you hit *2(view trouble)?
Those Batteries are 12 Volt, 7 Ah, will plug back in.
After that you will likely have a low Battery trouble and Loss of time and date trouble, after charging a bit, the low battery trouble will be gone, you will need to set the time and date to eleminate the other trouble.