My first suspect was what Iowaboy suggested, a fuel shutoff solenoid.
I looked at the parts diagram, and I don’t see that this engine has one, however.
https://shop.briggsandstratton.com/pages/parts-lookup#/Briggs_%26_Stratton/15C134-3023-F8/Carburetor%2c_Fuel_Supply/15C1343023F8/39460005/y
If you’re getting spark, then you’re not getting fuel. I don’t see the point in using starting fluid, all that’s going to prove is what you already know. You have spark and you don’t have fuel.
I’d check:
– Pull the fuel line off the carb and check to see fuel is flowing through line when the shutoff valve is turned on.
– Pull the motor over a dozen or so times. Remove plug. Does it smell like gas? If not….
– Check the carb’s float bowl. Usually, you can remove these without removing the carb from the engine just by unthreading the mail jet at the bottom of the bowl. Is there fuel in the float bowl or is it dry?
To be honest, I’d just pull off the whole carb and give it a complete clean if you know how to do it. A good marinade in zesty carb cleaner is probably the solution. Rather than try to piecemeal diagnose this thing, I’d just try to cut to the chase.