Predator generator will not stay running

Picked up a used Predator (4000) watt generator for super cheap ($30).  Physically in great condition for the most part.
It would barely run.  Tried cleaning the carb... no dice.
Ordered a brand new carb (complete) on Amazon.  Same thing.  Would not really start.  Was trying to hit, but no dice.  Would very weakly try to run for a couple seconds and die.
 
So I did some research.  Seemed like compression was low.  So I popped the valve cover and checked the lash - the exhaust valve was not even being allowed to close all the way!  Adjusted it to within spec and put it all back together.  When adjusting, I carefully rotated on the intake stroke and waited until the exhaust valve "blipped" over the compression release nib.  As far as I can assume, it was NOT on the compression release nib when adjusted.
 
Now when I choke it and give it a pull, I get INSTANT and STRONG fire first pull.   Like it wants to take off like a bandit.  But this only lasts 2-4 short seconds before it quickly dies.  When it dies, I can hear a bunch of pressure still being released (sounds like it may be coming through the muffler) for 3-5 more seconds.
 
A subsequent pull of the rope (with the choke on, of coarse) yields the same result. Over and over.  Starts strong first half-pull and dies.  Does not matter if you try to take the choke off or not.  Same result.
 
I thought, maybe the new carb is not adjusted correctly, but the small jet adjustment made no difference.
 
Additionally, I did a complete clean on the OLD carb and re-installed it.  Exact same result.  Starts instantly first half-pull but quickly dies and after it dies... lets out a hissing sound for 2-4 seconds.
 
Any ideas?