I've had trouble with my GCV for almost a decade. Started fine the first year, but every year after, it seems like it isn't (auto) choking. I replaced the wax pellet last year, and it didn't help at all.
The funny thing was that every time I removed and disassembled the carb, that first start after would work! But 10 minutes later-no go.
I think the float level is too low, but it's a one-piece plastic float, and no way to adjust the float level. I considered melting a hole in the top of the float, and adding solder inside, but don't know how to reseal the hole to ensure the float doesn't fill up with gas when running the engine.
Now I tilt the mower up on left side wheels at 45 degrees, until gas just dribbles out the carb. Then tilting at 45 degrees right, the engine will start.
I probable should drill a hole in the air filter housing, so I can just squirt gas into the carb mouth...