They can be temperamental bastids when not used regularly. I doubt it's timing or HT related as it was running when you switched it off. Check that mice haven't nibbled the fuel line, plunger bulb or HT lead. Timing is only usually an issue if you've hit something hard with the blade, which sheers the woodruff key, and then the crankshaft slips out of place to the timing plate.
Normally a good spin with the starter rope is enough to get them going but carb issues are generally the culprit. You also have to be careful which way you tip a petrol mower as the oil will find every little hole in the engine. My wife tipped our Toro on its front to free the blade from clogged grass and then wondered why it wouldn't start again. I cleaned the carb and tried starting it until my shoulder gave up. Luckily, when you remove the top cover of a Toro you can see the crank nut that the rope coil sits on. A socket on an adapted extension, fitted in a decent drill, will start it in seconds if all is ok. Dangerous but effective.
Carbs don't wear out as they are such low pressure fuel flow on these, but many change them as they think it's the cure. I'm yet to replace one, even on mowers over thirty years old. What engine is it, Briggs and Stratton ?? if so, what series is it (Usually on the engine cover) as I need to know what carb it has on it. Some are a resonating fuel diaphragm, and some have a proper bowl. The resonating diaphragm can be manipulated by hand to give it movement, as they go a bit stiff when not used regularly.
Are you using the rope pull in the rope guide on the handle. If so, remove the rope from the handle guide and pull from the engine as you get more revolutions per pull.