Hirsch - after you hit the primer a few times, does the engine at least try to start?
If not: Make sure the ignition key is on, or inserted on a Tecumseh (RED plastic key). Make sure the fuel valve is OPEN.
The float could be stuck. You could try tapping on the carb bowl lightly with a screwdriver. However, if this cures it, rest assured the problem will resurface at a later date.
The engine should at least sputter or run briefly on the fuel from the primer. I suspect a stuck float and/or needle. If you tilt the machine on the auger rakes & secure it overhead with a strap, you can access the carb bowl without removing the heat shield tin box. This may also keep the parts from just falling out, but there is still a chance they might fall. Have a can of carb cleaner, a small wire & rags handy. Run the wire thru the bowl nut holes & thru the tube that is ABOVE the bowl nut in the carb body. Clean everything well with carb cleaner.
Let us know how you make out...
Marty