I just fixed one with a similar problem.The choke mechanism was not working at all.I had to replace it with a new one.Find out if its electric or manual.If you have a manual remove and soak in degreaser then lubricate and install.the electric one has a solenoid so you will need to replace the unit.Also you can raise the idle a little bit to help with cold starts.Check mixture screws on carb and adjust.check fuel filter and lines.