When ever a bike starts normally, but then dies when the bike is moved, I suspect an ignition problem. And Kawi's are known for their safety switches that shut off the ignition. If a bike sat for a long time with the kickstand down, I would suspect the kickstand safety switch. Could also be the neutral switch, the emergency switch, clutch switch, ignition switch, or any of the connectors between said switches.
If it was my bike, when it died, I would pull a plug wire and connect it to an old spark plug laying on the engine. If it didn't fire immediately when cranked, it's an ignition problem.
Even better, I have an old timing light. Connected over any spark plug wire, it will tell you if that wire is getting spark. Plus, no one ever checks the ignition timing anymore, assuming that electronic ignition is infallible. I've had two of the spark units (ignition advance) fail on my CBR. The ignition stays at TDC, and the bike accelerates slowly, and everybody thinks the problem is the carbs. Nobody knew what the problem was until I checked the ignition timing.
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