Fastrak carb problems

[srbr]

I have a six year old Fastrak with the 20 hp Honda motor-it was run out of gas and I can't get it to run except on full choke-have cleaned the carb three times-new fuel filter and plugs-am wondering if it might be the solenoid (??) attached to the carb and wired to 12V-does anyone know what the purpose is of this or have any other ideas?
Thanks

[mowerconsultant]

Can you hear the fuel solenoid click when the key is turned on? its purpose is to stop fuel being sucked into the main jet when the mower is turned off, also preventing back firing.
Is the external vent tube from the carburetor clean and free of debris?