Small Engine Troubleshooting Problems? Ask a Mechanic Now.
First thing, run a cylinder test. Loosen the spark plug wires, and with engine idling, pull one wire off at a time. If engine dies when either is removed, the opposite cylinder is not firing.
Check for spark and compression.
If cylinders are ok, then check the solenoid in the carburetor. It plugs the main jet when it is closed. It has to open as soon as the key is turned on, and has to stay open.
Best test is to remove it and plug the hole for test.
These are the two things to begin with.