Pic is too small for me to make out the model #...
Did you pull out the main jet to make sure it was clear?
Squirt carb or brake cleaner thru all the orifices (and have it come out somewhere)?
**Did you try removing the air cleaner and spraying some starting fluid down the carb just before starting?
If it's a fueling issue, it light off momentarily.
You also mentioned solenoid earlier. You pic doesn't show a shut off solenoid attached to the bottom of the fuel bowl, or am I just missing it? The solenoids do have a habit of clogging the fuel flow, but I don't think you have one..
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