Its pretty unreliable to pour gas down the carb as baically you are flooding it then trying to lean it out by cranking it and hoping its catches when the fuel mixture is right.
You said it coughed so I'm guessing that its firing. You can check by removing one spark plug lead and putting a spark plug in it and laying it across something well grounded and clean. Watch it while some cranks it over and see if it sparks.
You should be getting fuel to the carb when cranking. If you aren't then either the pump is bad or the pump isn't getting fuel(bad line, plugged line, pickup broken off...).
How much fuel is in the tank? Could the tank be empty and the guage be off? Throw a can of gas in it.
I had a friend with a J20 that had rusty/cracked fuel lines. Occsionally it would suck air and die, took forever to figure out....