Good news on defeating the mice! If you have power in your shed, the best advice I can give you is to use a Battery Tender Junior to keep your battery fully charged. Keep it plugged in whenever you are not driving it. It will not overcharge your battery, and will greatly extend its life. I would try the Battery Tender Junior with your existing battery and see how that works before getting a new battery. If you do get a new battery, the AGM style is the best. They hold up very well in rugged use.