Re: those check valves, you also have to be judicious where you blow compressed air. It too can damage those check valves by unseating and/or blowing the rubber out.
To the OP. This will sound crazy, but if you have an extra ignition unit around, try it. Also discharge test your battery, and run the ignition straight to the battery eliminating any electronics or switches you might have. I once had an engine that acts exactly as you describe, and it turned out to be the ignition. When I tried a 6 volt battery instead of my 4.8, the engine started and ran normally. I got the tip from Bill at CH Ignitions. At any rate, it wouldn't take much to try it and eliminate it as a possible culprit.
AV8TOR