Someone mentioned it before about the exhaust possibly being restricted. When I was young I was given a moped 2 stroke. I worked and worked on it but it would not start. I had the exhaust pipe off of it and for some reason tried to start it and it started. Turned out the entire exhaust muffler was full of carbon. I hacked sawed it in to two pieces and removed all the carbon then had it brazed back together and it was fixed. Same thing happened to my lawn boy it would not start and the exhaust muffler which is under motor and mowing deck was full of carbon and it to would not start. Neither motor would as you say pop off and both had spark and fuel.
Since your waiting on points you might consider checking to make sure your exhaust is clear.
Hope that helps,