Hi and welcome to FixYa,
Initially, determine the quantity and quality of the fuel by loosening the drain screw and catching the fuel draining. Additionally, determine if there is spark right after "engine bogs up then shuts down".
The "quantity and quality of the fuel" would be indicative if the fuel is contaminated and/or if there is sufficient fuel in the carb's bowl to run the engine above 10 seconds. Checking for the presence / absence of spark after the engine quits would help you determine if it is an electrical problem or a fuel starvation issue.
Good luck and thank you for asking FixYa.
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