only if I push it?

My bike will only start if I push it, and very easily. when I try the
electronic ignition I get nothing. I have replaced the battery and
plugs. when I use the starter it turns,but the bike doesn't want to
fire over. after running the battery down in attempt to start it I
will go to the street and push it and the beast will come alive so
easily.

Why won't the starter kick it over?

It is on a 86 ninja zx600.

 

Maybe the the voltage drops too much when the starter is turning so the
electronic ignition won't operate? Some other posters have suggested
that this can happen. Check all the electrical connections from the
ignition switch, through the kill switch to the coils and on to the
electronic ignition module to see if you have 12 volts everywhere.
Check all connections to be sure they are clean and tight.

OTOH, you might be running into a problem with Kawasaki's diabolical
sidestand safety interlock system. When you are pushing the starter
button, are you sitting on the motorcycle with the sidestand up, and
pulling in the clutch and the starter is spinning the engine madly but
it doesn't fire?

Kawasakis are wired so the starter will crank the engine over but you
won't get any spark if the sidestand is down or the sidestand safety
interlock switch doesn't work right.

Or, are you standing beside the motorcycle with the sidestand down and
trying to start the engine?

Try disconnecting the sidestand switch and jumpering across the two
pins of the connector coming from the motorbike's wiring harness and
see if the engine starts.

I have jumpered the connector on my Kawasaki duel sport after the
sidestand switch gave me a lot of trouble.

Then there is the possibility that your carburetors have dirty idle
jets. When the idle jets get all gummed up, the engine will stall and
the owner will adjust the idle speed screw to make the engine idle
faster.

The problem with doing that is the engine becomes very hard to start
because the throttle butterflies are open too far. There isn't enough
engine vacuum to suck mixture through the starting enrichener bypass
system.

You can clean the carburetors out by putting 3 or 4 ounces of
Berryman's B-12 Chemtool Choke and Carburetor Cleaner in a full tank of
gasoline and riding slowly until the engine idle speed increases. That
means the B-12 is cleaning out the idle jets and you can adjust the
idle speed lower by turning the master idle knob.

If you live in a part of the world where you call gasoline "petrol",
look for a carburetor cleaner that contains xylene, acetone, and methyl
alcohol, or maybe toluene to clean your carbs while you ride.