I have a 16.5 HP snapper riding mower with a key start up switch. The batter would not hold a charge so I replaced with a new one. It started fine the first time, but after cutting grass once and then parking it for a week the mower won't start again, plugged a battery charger to it and started it that way. There is something that seems to be draining the battery even when not on. Could it be the starter or ignition switch itself.

Probably the battery has a dead cell.

Probably the battery has a dead cell.
Battery is brand new and the previous battery lasted for years without this problem. The starter got stuck on before changing to a new battery so I am thinking it is either the starter going bad or the ignition switch itself.