17.5 B&S won't start after running out of gas

My son in law ran out of gas and mower wouldn't start back up. Skip all the usual troubleshooting, finally replaced the carb. Now the only way the mower will run is holding hand over the intake to choke it. As soon as you allow a little air by moving a finger just a tiny amount, the engine dies. I've got good fuel flow to the carb, good fuel flow in the bowl of the carb. I'm lost now.

Clogged main jet in carb, or fuel solenoid not working. Could also be unrelated to the carb or fuel, and something has effected the compression of the engine leading to what looks like a fuel issue. Even some of the newer ignition module can cause an effect like you are seeing.