Car wont stare new battery but drainig air filter laying to side do i need a new

Hello, The battery is draining because of cranking with the engine off. I need a couple things answered to understand the situation. Why was the battery replaced? What is happening with the air filter? If the vehicle will not start with a full battery, the alternator is not likely the issue. http://repairpal.com/honda-within-10-miles-of-washougal-washington-98671