there are 3 things that any engine needs to work. Compression, spark at the correct time, and air to fuel mixture. Fuel ages so something sitting all winter doesn't behave like fresh fuel. I personally have found the best way to start any pull engine is to prime it when not fully warm, pull the rope slowly until the engine resists a bit then pull hard, or if the rope is too far out, let it in and pull hard. Doing that my Toro or Edger etc will start almost the first pull each time. I used to rebuild the carbs on anything I owned with great success, but finding good quality parts have been harder so I try to find a new old stock carb when i can now, replace, and rebuild the old one as a spare at my convenience. Older mowers and small engines tend to loosen the head gaskets over time and that can cause issues. So can tight valves on high use engines. Ethanol in the fuel can cause issues. Many years ago I had a boat whose engine did not behave properly and I spent hours on it. I discounted that the fuel was bad because it was only about 60 days old. In the end the problem was the fuel was stale. The point being, don't discount the small things. Figure what of the three items is missing when something won't start before throwing parts at it.