You mention not starting, but then go into changing a battery, jumping to alternator...so I take it you mean its not CRANKING , not starting is a whole separate problem....

Check battery draw with it shut off using an ammeter, should be virtually or no load (pending things such as a radio memory circuit, etc. If you dont have one or arent sure, try leaving it set a few days with the battery disconnected after making sure its charged. Thatll tell you right away if you have a draw problem, many possibilities.