If your reticulation isn’t working then changing the battery will just be $9 down the drain.
The battery is not responsible for the operation of the sprinklers. It simply helps to retain the settings when the power goes off.
Your retic needs 24v if power to open the solenoids so changing a battery wont do the job.
If it’s not working then it could be any one of a number of issues – but it won’t be the battery!