Check the automatic choke to ensure that the choke valve is closing prior to attempting to start and staying closed while cranking. You could try adjusting the choke to be more severe until you resolve the starting issue. It being set more severe will make it run rich but as long as it opens partially when running at no load (not driving) it should not create any issues.
If you a low pressure air source (say 5 psi or so) remove the idle needle and blow air into the passage the screw is removed from to see if you can dislodge any blockage in the idle circuit.