So the battery will not effect the bike's ability to start?
I guess I'll start looking elsewhere for the reason why it won't start. I tried kick-starting it many times, tried to pop the clutch with the bike rolling. It sounded like it wanted to start but never did catch and actually run. I guess I'll replace the air filter and go from there. This is my first time working on anything with a carb, so it will be a learning experience.