Thank you all for the suggestions, it's taken me a while to find time to respond. Since my last post I did remove the blot holding on the float bowl while the carb was on the mower. Gas began to run out until I shut off the fuel tank. I may try to run a straight fuel line from the tank and bypass the fuel filter next.
unclelee - I did what you suggested. I removed the muffler and cleaned the exhaust ports. I'd say they were about 10% clogged. It didn't look to me like that would have prevented it. I removed and tore down the carb again. The main jet appears to be pressed in. I couldn't remove it. I tried to pull it out with needle nose pliers, but it felt like that was going to do more damage than good. This is the first carburetor I can remember that doesn't have a main jet that unscrews. Carb cleaner blows through the main jet and out into the air horn (or body, not sure what you would call it) with out restriction it appears.
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lewb -
Thank you for the suggestion for checking the float. I'll try just that although I'm not sure how well the plastic tab on the float will bend. I'll also check the compression.
motoman - I'll keep that wire trick in mind and see if that might help. I did have the mower in choke position when I tried to start it. The choke flap is working.
After looking up some parts diagrams, I see some carbs similar to this one have an inlet screen for a filter. I'm 99% sure if this one had it, I removed it years ago. I don't remember any screen being there when I tore it apart, but I'll check one more time.
Thank you again for all your advice. The mower runs briefly on starter fluid, so I'm fairly certain it's not electrical/ spark of exhaust port related.