Choke does not matter as it is before the fuel venturi.
Worst it will do is allow dust into the engine and not open/close fully.
If you post the model and type numbers some of thoes in the trade might do a double check that you got the right rebuild kit.
In the mean time slip the float bowl off, put a container under the carb, turn the fuel on and work the float up & down to check that it both lets in fuel & cuts off the fuel supply when in the level position.
Now we get to silly things.
Is the fuel tank and lines clean ?
Do you have the correct fuel filter ? The gravity feed filters are different to the pump filters and fitting a too fine filter can slow down the fuel just enough to starve the engine.
does it have a fuel pump ?
did the original engine have a fuel pump?