points? unhook the coil and see if it has spark then. if it does there is a short in wiring to frame somewhere. is there resistance on the pull rope? it is possible it may have broken a connecting rod.
Remove spark plug and try to pull. There could be water on top of cylinder. Would replace rope before you beeak as it will be easier to see how it is wound etc. There should be many videos online showing you how.
You may have motor internal problems with governor control. Moving governor arm from engine and see if it operates freely if not try pecking on shaft that does into engine and see if that might free up.
The only thing that stops gas going into the carb is the needle valve and seat in the bowl of the carb.
Doing the same thing with 2 different carbs sounds like trash in the gas tank flowed into the carb and is holding the needle valve off the seat allowing gas to flow all the time.
Clean the tank. Clean the trash out of the needle valve/seat. Add a small engine fuel filter between the tank and carb.
You should be good to go.
When you installed the new carb did you adjust it for your engine? Idle control, idle mixture, fast misture? Running only with choke indicates that engine is not getting enough gas routinely via the main jet.
I show how to do the annual maintenance on this push mower. This includes changing Oil, Spark Plug & Air Filter on a Troy-Bilt TB110 push mower with a Briggs & Stratton 550EX engine.
