It very well might be the battery, but also make sure that the battery cables are securely screwed on to the terminals. A loose cable can make it behave as you describe (starting once, working intermittently, etc.) To bump-start a bike, it's usually better to be in 2nd gear rather than 1st. You need to get the bike up to a decent running clip, and drop the clutch while in gear. The hard part with kawi's is the positive neutral finder won't let the transmission shift to 2nd unless the drivetrain is moving fast enough.
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