you say you pulled the carb did you take it apart as well to make sure it clean... or just blow air at it?
thinking likely your float is stuck closed..... or your fuel pump is sticky
suggest before you tear into it anymore... since you likely have carb back on... try this.... prime engine with primer bulb... use squirt bottle and squirt 50-1 mix straight down the carb to prime block..... make sure your engine has water supply and try to start.
it should fire on the mix squirted right down the carb. this should make for much better pulses hitting fuel pump... and perhaps free things up. then if engine will not catch by self and perform properly... clean fuel pump and carb well with complete careful disassembly and very thorough cleaning.
a few other things to look for...

kinked fuel line, primer bulb backwards, and collapsed or squashed fuel line.
Personally i don't subscribe to the run out of fuel to store it, while that last bit of fuel is running out the oil/lube is also going...... dont think it is healthy for the engine.
Sean