You said that you have good compression. What is it? It should be around 65-70 psi even with the decomp active, 120+psi with it disabled. If below 65 psi I would be suspecting either worn cylinder and a bad valve. I had one generator here that was low hours that the cylinder was worn out and ovaled. When I honed to the oversized .020" the oval didn't clear until .019".
Because it runs once started it should eliminate the ignition and fuel as being the problem. All left is compression problems.
