Small Engine Troubleshooting Problems? Ask a Mechanic Now.
have you tried removing the air cleaner and seeing if it'll start up without it?
as its possible that water has gotten into the air cleaner and swollen the filter?
If this is OK then I'd check that auto choke mechanism on the carb is functioning correctly
OK this sounds like the fuel passage / jetting isn't getting enough air
there's a air mixture jet and gallery that sounds like it may be blocked up so preventing air being drawn over hte main jet
so when you hand choke it you throttle the air flow enough to generate a larger vacuum than normal and start pulling enough air over the main jet and so drawing fuel
so I'd check the main venturi in the carb and its air passages are clear which are usually fed with a jet that needs clearing out