You took the carb apart, including the mixture screws and fuel valve and cleaned in carb cleaner, right? I suspect the fuel valve is hanging up.
Usually there are two mixture screws. The large for fast idle and the smaller on for slow idle. Turn them in all the way and back out 1.5 turns for the initial start. Then adjust fast and slow idle.
Your throttle linkage is hanging up or a spring is missing. The flywheel is a small fan which helps cool the engine, but it has another use. The air pressure from the blower moves a flap which moves the linkage on the carb. Keeping the speed relatively constant.
Check the parts diagram on
Home - Briggs & Stratton to see if you missed anything.
A rebuild kit will set you back about $15, but you should not need it unless the diaphram is bad (assuming this is a diaphram carb).
No new carb.