As it will run on starter fluid the prime suspect is fuel
1) remove the fuel line from the carburettor and hold it over a reasonably big container, about a quart or better,
Get her to crank the engine and check for a strong fuel flow.
It will splutter a little because the engine is turning over at cranking speeds & not running speeds.
2) if above was OK then remove float bowl and crank for a few seconds while working the float with your fingers to check the fuel is flowing through the float valve and gets cut off before the float touches the carb body
3) check what came out above for water , fine particulates , etc
Have a real good look & smell of the fuel for freshness & quality
4) after that it only leaves the fuel solenoid.
a bit harder for home owners to check other than turning the ignition on & off and listening / feeling for the clicks as it opens & closes.
I check them visually with the engine static and in operation by replacing the solenoid with a plug / bolt and an O ring to make a seal.
The solenoids themselves rarely fail but the wiring to them does , particularly on ZTR's
