It is a case of elimination
By removing the belts we eliminate the mower putting a drag on the engine
When running along a slope it is easy to have the oil pick up in the air so the oil pump is pumping foam or just air
The top bushing area has a small dam of oil and if it is not kept full then the crankshaft can sieze in the crankcase
Or the starter motor can jamb which normally releases by rotating the flywheel backwards.
A 2002 model is well past its use by date but we are here to fix things if that is at all possible
Usually side valve engines loose valve lash on the exhaust because the valve seat burns away
All side valve engines do this and when it gets chronic the exhaust valve no longer seals
It is a PIA on side bangers to check because the valve chest is behind the carburettor.
In the workshop I have both a bore-o-scope & a leak down tester to check for this .
If the valves can close & the timing is good then the engine will fire when you put fuel down the plug hole
If it does not fire then either the valves are not sealing or the flywheel has spun on the crankshaft so the spark is out of time
or the piston is no longer going up & down.( check with a pencil poked down the plug hole .)
If the engine had a temporary seizure & you forced it free by turning the flywheel then there is a good chance the timing key broke or the con rod broke
So try what has been sugested and come back
-It can't hurt removing the belt, I'll try that from now on
-The starter motor is good: it spins, goes up when starting, and goes back down when off.
-Unsure of the valve condition, will check
-I think the con rod is fine, I can feel some compression and see the piston moving up and down.
-The timing key/magnet is quite rusty but is still magnetic and hasn't broken. It's possible it became offset though, however it doesn't seem to fire at all, forget misfiring.
In a bit I'll try removing the belt, putting fuel directly in the spark plug hole, then checking the valves.
I've also seen people have a similar starting issue, which is caused by safety switches which prevent the engine starting if the deck is down for example. The switches can get stuck and make it think it's still down when it's up. I've tried starting it while one of the switches is disconnected, no luck, but there may be other switches I'm unaware of.