I have a 2004 Scag with a 19HP Kawasaki. First of all, how can I tell if the alternator is working? If it's not where it is found on the engine? The original battery died about a month ago. I assumed it was due to the cold weather. I purchased a new one. It worked fine for about 3 weeks. The it had to jumped off again and again. I took the new battery, had it checked, and it tested good. They replaced it anyway. I haven't tried the new battery yet, as I just got it replaced late last night. Any ideas?