The CDI unit himself is ok, I know thats not that.
-good we agree on that
The "bobine" is the device that transform the 12V to the voltage for your spark plug( in dutch called Bobijn, so I thought in englisch bobine, because I do not know an other word for the Bobine, I will use it in the lower text.)
-this sounds like the COIL if its the coil i dont think that would cause it either since it runs fine being push started
The spark plug need a minimume voltage to ignite the air/fuel mixture. It is possible that there is not enough energy to ignite the mixture however you can see the blue pulse on the spark plug.
-is it a nice big spark or very light/weak spark ?
So what I thout was that when you kick, during the short time it doesn't make enough voltage. But when you push the bike it's maybe possible that the bike can make a stable voltage and nevertheless starts.
I can check the voltage over the "bobine" but I don't know what the ideal voltage is to compare with. I haven't tested it yet because I do not have device to measure it so I don't know whats it is on the moment.
-figure out the part name and i can tell you how to check it. i think your talking about the coil but dont know for sure ?
you will need a multi-meter to test the coil
The bike doesn't have a battery, thats why I think it could be unstable.
I don't know if it's a AC or DC CDI unit, how can you see that.
-since it doesnt have a battery it is considered an AC CDI
Srr for my bad english and I hope you can make something out of it. The thing I describe above is what I thought, but i'm totaly not sure, so i asked here. It could be totaly something else.
-your english isnt too bad. i understand most of what your saying other BOBINE ???
thanx