B&S 19.5 hp twin won't start after repair

Pardon the long post. Drove the tractor into the shop. Smoking bad. Rings? Valve guide seals? head gasket? failed breather?
Took it apart. Cylinder bores measure 2.9693. New bores spec at 2.969/2.970. Didn't think I needed to check the rings. Replaced the head gaskets and valve guide seals. Re and Re the breather and checked its operation. Bolted everything back together and set the valve lash. The engine would not start. Good spark on both cylinders. Compression measures 105 and 118 psi. I can hear the fuel cutoff solenoid clicking on turn on. Plugs come out wet after trying to start. Will not even respond to starting fluid. Does anyone have an idea where I can go with this ?
Update : The tractor will run if you pour a lot of gasoline into the carburetor. The carb is almost new. The float bowl is full. The anti after-fire valve is working correctly. The inside of the carburetor is immaculate and the passages are clear (jets, emulsion tube, etc.). It won't start or continue to run even on full choke so I am still flummoxed. Any suggestions are appreciated.

You see spark at the plugs grounded to the headS?
 
Did it start smoking alot all of a sudden, or a slow build up?
Were the piston tops and heads gunked up with oil or carbon?
 
As there's no kick with starting fluid, check the flywheel to crank key,
that it's not sheared..
 
Also, a full engine model # would help.  
 
I would also do a leak down test as the heads are back on. 
Leak down shouldn't be more than 15-20% at 100 PSI.
 
.

Thanks Scott
                    I purchased the tractor recently so I don't know what was the nature of the history. Yes, big fat sparks. The pistons and the heads were gunked up with soft oily deposits. The engine is a 407577. I posted an edit before I saw your reply. It will run with a steady stream of gasoline into the carburetor (1/16 diameter hole in the top of a plastic oil bottle.  but will not start or run even on full choke. Carb situation is in the edit. I don't have a leak down test kit. I can only check compression. I will get a kit. Thanks again for your help.
Bob

Ok, so it's now narrowed down to fuel, IE, the carb
 
https://jackssmallengines.com/jacks-parts-lookup/manufacturer/briggs-stratton/briggs-stratton-engine/400000-699999-series/407500-to-407599/407577-0292-e1/carburetor-exhaust-system-fuel-supply-kit-carburetor-overhaul
 
Part # 117 is the main jet.  It resides in the bottom of 137a.  It is tiny and DOES clog easily. 
The jet, as I re-call is smaller on one end so pay attention to that.  
 
The bowl gasket, if hit with carb cleaner will make it un-usable.  
 
As that is the main issue usually, check to make sure the float needle is opening and not stuck 
closed.  
 
You can often just remove the bowl, leave the plastic, # 137a in the main carb.  
At the very tip (would be at the bottom of the float bowl) INSIDE 137 would be that jet.
 
A jet cleaner or very fine piece of wire (from a wire brush held with a vise grip), you should be able to 
push it thru and clean out the jet (W/O further disassembly)..
 
.
 

Carb should be similar to this: