That engine only needs 3 things to start... A mist of fuel and air, a good spark and decent compression.
You already know it's got compression because it hydraulic'd when the cylinder was full of fuel.
You've already checked for a spark?... if not there are a couple of things that can cause 'no spark' like oil alert switch, magneto gap (older engines) HT lead or cap. Or simply a duff spark plug.
So that just leaves fuel/air which is why the carb is the No1 suspect.
Remove the carb, give it a good clean. Blow all the jets out with compressed air including the one under the needle in the float chamber (unscrew it out of the pick up tube) Then just inside the ventouri there are four tiny holes, you can hardly see them they are so small. Pull a strand out of a wire brush, bend it 90degrees and poke it through the holes. If they are blocked it won't run.
Re-assemble then turn both the air and mixture screws all the way in... then turn them out one and a half turns (this will give you a starting point for fine adjustment once it's running.
Before you start it, make sure the fuel is good. By that I mean does it smell like petrol or has it gone off? it will smell like an old tin of varnish if it's bad.