Check the accelerator pump operation.
Make sure that with the engine off looking into the carby that when you give it full throttle that a jet off fuel is getting sprayed in to the carb.
If not - and its been sitting around for some time, the accel pump plunger may have perforated or split.
Also if you ever suspect the shutoff solenoid - it just has to have 12volts to it when the ignition is on. If you ever think its a problem take it off and remove the guts and reinstall it - just to make sure it hasn't become stuck.
Hope some of this helps.