Get a can of starter fluid and an in line spark tester.
With install the spark tester and remove the wire from the bottom of the carburettor so fuel does not get drawn in.
If yours is the twin tank version turn the fuel off.
Remove air filter and squirt a LITTLE SHORT SHOT of starter fluid in while cranking the engine and watching the spark tester.
Unless you have real long arms you will need a helper to do that.
If it starts continue with short shots of starter fluid for around a minute, just long enough to prove you can keep it running.
No spark from the tester = electrical problem
Starts and runs = fuel supply problem
Wont start with spark
1) remove rocker cover and check operation of valves
2) remove blower housing and check flywheel key.
I find the "Sparkrite" type of tester works best , is cheap and can be fitted permenantly .
On ZTR's with exposed engines look "cool" ( sick if you are a bit younger ) flashing while the engine is running.