Never had a two-stroke yet that if it had spark did not fire when dripping a couple drops of fuel in the spark plug hole. May have to do it a couple times. Do not overdo it and it will fire. Once firing, they usually suck up fuel thru the carb and then its good to go for the season. If not, then the carb screen or filter is plugged enough to prevent it from running. Yep, fuel can be drippin' from the carb but not getting up into the cylinder.
Once, I even have had clear debris sitting on the carb's screen and it looked clean. But, the screen was not clean until it was removed and I blew air thru it. Looked like something came from inside the fuel line or carb itself. Maybe old fuel or manufacturing foreign material. Got nearly 50 years experience froggin' around with 2-strokes. When they don't run/start right, start with cleaning the carb and you may even have to do it a couple times.
Should have a filter right before the carb inlet. If you don't the carb is the filter.
Also I had a brand new Dubro large scale gas filler valve's O-ring fail. If you plumb it as the valve instructions suggests, when the O-ring fails, the engine sucks air thru the valve and the o-ring particles wind up downstream. I have since gone to three line systems just using the valves for filling with the downstream line plugged. Have had an O-ring failure at least once a year. Eventually converting all these over to fuel dots.
Had a 2-stroke last week that would not start nor adjust correctly. The owner was using 92 octane gas and had the wrong oil mixture. Once the fuel was replaced, the engine started right up and dialed right in. I always use 87 octane gas. It has more BTUs resulting in more power and it is what the engine design calls for. Most of the additives in 92, do not burn.
For a quick test of tank and plumbing, one can use an overflow tank plumbed directly to the carb. Also, drops of the fuel in the spark plug hole will prove whether or not you have enough spark.