Need some Mechanical Help Non-Speedster

Do those have an air filter?  Maybe it's clogged and not getting Any air?

Just guessing here, but do you have a diaphram ( sp ?) type fuel pump ? Maybe not enough fuel going to run the engine properly but after shutdown it may leak enough thru the pump to fill up the filter a bit. And like Todd says...check the air filter too.

What did you maybe wind up into the blade clutch? I'd see if maybe you're missing a jumprope or wad of bailing wire.

Check the pressure switch under the seat. 

Still sounds like fuel starvation, so try this:  You'll need either an air compressor (set at about 40 psi) or a can of Gumout Carb Cleaner and I'm taking this approach because you say that you have spark when you try to start it.

1.  Remove the air cleaner

2.  Turn off the gas at the tank - if it has no shut-off, pinch the fuel line lightly with vice grips

3.  Remove the fuel line at the carb and then remove the float bowl

4.  If it has hi/lo mixture adjustment screws, remove them (note which is which and also watch out for o-rings on the screws and don't lose them

5.  Using the carb cleaner or compressed air, spray into the two mixture screw holes for about 5 seconds each.  Watch for where the spray comes out of other carb ports and spray into each of those ports, too - 5 seconds each.

6.  If You have compressed air, blow into the fuel inlet (where the fuel line was).  Loosen the gas tank cap and blow into the end of the fuel line for 1-2 seconds a couple of times about 5 seconds apart.

7.  Put everything back together.  GENTLY bottom out the mixture screws, then turn them out 1-1/2 turns each.

8.  Turn on your gas at the tank and try starting it up.

If that doesn't cure it, then it's time to take it to the repair shop.

When you blow out the fuel line up through the tank, make sure you open the shut-off or remove the vice grips, then close/re-vice grip the shutoff.  You just want to make sure no crud is caught in the hose.

Gordon is on the right path.  I bet the jets got clogged. Is it a Briggs  & Stratton, Tecumseh. or a Coulter engine  .

So here's what I found...... The carb is gravity fed by the tank being mounted  higher. There was sufficient flow to fill the fuel filter partial and in turn the carb, but don't think it was enough to run it. (Of course I still think it should have fired on starting fluid).  I replaced the fuel line, the fuel filter fills quicker and changed the plug for good measures (even though the other had spark) put it back together and Wo La...... it ran........... go figure? Thanks everyone for thier imput and sugestions

 remove the bowel on the carb again a in the very center is a jet  unscrew and clean it.. I BET ITS FULL OF CRUDDY ,,, E 10 GAS  GOOP! .

 USE SOME CARB CLEANER UP INSIDE THAT PASSAGE AND WASH IT OUT GOOOD