Echo pb403-h saved from the dump…wont start

Check that the flywheel key hasn't sheared.  You can get an "idea" if it's close just by finding TDC with the piston and where the magnet is to the coil.
 
It could have leaky lower seals but try a couple teaspoons of 2 stroke oil down the cylinder (helps seal up the rings) and try starting.  Best to try with the muffler completely off.  You can also inspect the ft of the piston skirt with the muffler off.
 
I don't remember if the coil can be installed backwards, if so, check for that.
 
With the new carb on it, double check the intake manifold is installed correctly and with gaskets... 
You don't what was done so most everything must be checked.
 
.

Quote:
Questions from the learning novice:
Piston is moving up and down, getting spark from magneto/coil.  Could the flywheel key be sheared?
 
with 110psi of compression, could the lower seals be leaky?
 
I will double check the carb installation.
 
Isn’t it strange that with spark, the starter fluid doesnt even get a pop? " End quote
 
Obviously, the main internals are fine but yes, the keyway can be sheared.  You don't know the history  of the engine nor the competence of who worked on it last.  
 
Again, the magnet on the flywheel should be very close to the coil when the engine is at TDC (piston as high as it goes)..
 
Not enough compression, a hole/leak in the crankcase will not allow starter fluid to get SUCKED into the crankcase, then pushed up to the combustion chamber. 
 
The added oil temporarily added does often help for the initial start. There should be one carb adjuster screw(not the idle adjustment).  If this adjustment is was out, that'll affect starting.
 
For now, try the oil (couple of teaspoons) and check the position of the flywheel magnet to the coil..
 
.

Will be back at it with your advice.  Sounds like some great ideas.  Thank you again in advance. Will keep you posted.  I’d love the get this thing running now even if for just the challenge.