I think you could have multiple problems going on at the same time :
The whirring noise is probably the starter motor running without the bendix extending : check your starter bendix, when driven, it should extend and engage its small gear with the gear teeth of your variator.... A little rust or dust will make it stick and it often works better after cleaning it anyway, so there's no effort wasted there... (you can lubricate it _very_ lightly with WD40 or just a drop of oil, don't turn it into a dust magnet again..)
The kick starter has a similar kind of friction system which extends a gear-like part when driven, that slide might also be stuck after a while of inactivity, same over here : clean it anyway, and lubricate it only very lightly to prevent excessive dust buildup.
When our scooters haven't been running for some time, the gasoline will have vapourized from the carb and it will be hard or impossible to start because the vacuum controlled petcock will only let gasoline flow when the engine is turned over pretty fast - even the electric starter has to work pretty good for this and it's almost impossible to achieve with the kickstarter - a quick cure sometimes is to take the small vacuum tube from the intake manifold and suck it for ten seconds or so...
Oh, and since we have a DC type CDI, which needs a steady 12V DC, the engine will simply not start with electric nor kickstart when the battery is empty or even undercharged...
