This tiller was toast. Cracked block,piston seized in its bore, gas tank full of water. So I welded the block, freed the piston, lapped the valves, replaced the head gskt. Cleaned out the tank, rebuilt the carb. (with new fuel pump,pick-up tube, mixture needle,and many hours of soaking.) Now it only runs on starting fluid. I also can keep it running by covering the intake then uncovering it when it starts to die. I tried the mixture screw in many positions, (even all the way out and in my hand) but this did not help it run on its own. I must be missing something simple!

The carburetor ahas many small vents and ports which are clogged. Try Bleach White, yes the tire cleaner on the carb, and use a very fine wire to probe every vent and orfice in the carb. And be careful, the Bleach White is caustic. When I worked in a small engine shop the symptoms you describe were 99% of the time a plugged carburetor. If you can't clean it out, it probably has some internal corrosion which indicates a replacement carb is needed... but don't give up easily, carbs can be a real pain.