Briggs Stratton 1980s 3.5hp horz w/ pulsajet; only cranks with starting fluid; runs great

I have a Briggs & Stratton horizontal shaft (from old McLane/Craftsman reel mower) with a Pulsa Jet carburetor.  I have a weird one in that the engine only cranks with starter fluid sprayed into carb, but once running ... it runs just fine.
The engine is 80202 0855-02 80032601.  
It has the carb with the plastic long & short pickup tubes (not the wire mesh/metal short pickup).  I looked at the material linked in other posts at "" but I could not decide what my problem is.
 
Whether engine is hot or cold - it does not fire/start unless I spray starting fluid.  But then it cranks right up and continues to run just fine.  So it is like on a pull start - there is not enough vacuum to pull fuel into the carb.  Or that is my best current hypothesis.  But I don't know why.
 
More history, the mower previously ran okay.  But it sat for years outside.  When I got it - it would not run.  I tore down carb and tank.  I had to rebuild tank as it was badly rusted.  (Yes - I split the tank and built a new reservoir cup, sealed it, etc ... spent soooo many hours on tank - I don't want to give up on this project).  I don't think the tank is the problem as the reservoir cup is holding fuel just fine.  I had replaced pulsa-jet diaphragm and spring just to be safe.  I thoroughly cleaned carb - removing idle screw and cleaning with carb cleaner.
 
I did have a spark problem where the old wire was cracked and shorting.  I shrink wrapped it.  And the points were not opening - so I adjusted and the spark looks good now.  There is a chance the points are a little wide - but since the engine runs once started - I didn't think that was it.  Unless the issue is the spark is only strong enough to ignite the ether in starting fluid - but not gas????  Hmmm..
 
So I guess it could be condenser or points.  Would appreciate any thoughts.
 

Thanks Scott.  I did try adjusting idle stop screw a little but will try again.  I do need a new spark plug - as I am running with the old one.  I guess I wasn't pursuing spark issues b/c it fired okay with starting-fluid.
 
I do not have a sonic cleaner big enough for the carb. I've been spraying carb cleaner throughout hoping to get things cleaned up.  The carb actually seemed to function well (pump worked, pickup screens not clogged, butterfly valve had good movement) with minimal cleaning.  The choke would stick open - but I worked it and it functions okay now.
 
When you've seen a good spark outside the chamber - but not inside - what do you attribute this to?  Gunky threads not grounding?  Bad plug that doesn't like to be horizontal but works when held down?
 
Question for anyone - on the bottom of the carb - next to the short pickup tube - there is a little port - that seems closed.  Is that anything that could play into this equation.

Hi Scott et al .. problem solved and ... you were right.  All it took was a $3.99 Champion spark plug.  Motor runs great now and starts up without cheater fluid.
Thanks so much for insisting I change the plug.  Lesson learned.
 
I did end up leaning out the jet adjustment screw so that it idles at 3600 rpms.  I think that is right for this mower.