If it's sat for a year or so with gas in it, more than likely it just needs a good cleaning. Remove the carb, then drop the fuel bowl, and look for sediment in the bowl. Get you a can of spray carb cleaner, and spray through all of the ports you can see. Also remove the fuel shut off needle & float, and make sure it's clean.
Do yourself a favor, and get a bottle of Stabil fuel additive stabilizer, and add it to the can/container you'll be using out of. It will stabilize the gas, keeping it fresh for 24 months. It prevent gum, and varnish buildup in the carb. Another good product is Seafoam. This product keeps the fuel system clean. I'm not much for products most would call "mechanic in a can", but these products work.
Since the introduction of ethanol in gas, it has wreaked havoc on just about all small engine, and older gas tractor carbs. Ethanol will attract moisture, leading to debris in the fuel system. Once you get the carb clean, adding these products should keep the fuel system clean. I have several David Bradley tractors I use in the garden. I add these additives to the fuel. All started this Spring, on 4 pulls or less. Not bad considering all have engines from the mid-50's, and the newest that had been repowered with engines from the 60's.
Your certain adequate fuel flow is getting to the carb? If so, did you pull the carb and flush out the fuel bowl and give the carb a good general cleaning? A small speck of gunk/dirt could be causing all your issues.