Pull the valve covers and look over the valves and pushrods. I am willing to be you have a bent push rod from a stuck valve. The stuck valves are usually caused by poor fuel or excessive cylinder head temp from being plugged with grass.
Zaq,
It's a two cylinder engine and has compression on both cylinders. That pretty much eliminates a bent push rod.
It has spark and gas, or starting fluid, and won't start.
Not much left after spark, compression and fuel, so it seems like timing, but that is flywheel controlled, so maybe its a bad module or coil, I don't know what those look like on that engine, but maybe it only has enough fire to spark when the plug is out of the engine.
Plugs can fail and short to ground from metal on the electrode. Happens a lot on dirt bikes, but they won't both fail at the exact same time.
I'm thinking it's in the ignition system. Coil or module.
One more thought. Some of those engines shut off by closing the throttle all the way, beyond idle to zero. Make sure the throttle is opening up when you do the starting fluid test. Choke open, throttle open, cranking and spry a heavy dose of fluid. Do that as a final test before tearing into it. Then start looking at ignition.