If you already have a new battery and its the maintenence free one and you fully charged the new battery with a battery charger I wouldn't think you need another new battery.
I would recharge the new battery with the battery and ground cables disconnected. Take a voltage reading of fully charged battery. Than reconnect your batt&ground and take another reading to see if your are getting a heavy draw of your fully charge batt. You will get some but only the radio, LP detector and electric steps but not that much that it will drain the batt down fast. You should also have a 5w solar panel to make up for the small drain form radio etc,etc.
Let us know how your making out.