A lead acid battery left alone will discharge at about 3% per month IIRC. So it's not so surprising that your unused battery is down. Try recharging it overnight. Your battery charger is unlikely to harm the battery when left on, but to save a bit of shore power cost, put a timer switch plug between it and the shore power.
A lot of boats have not only chargers but also dehumidifiers and even heaters running over the winter months.