After 2 years the carb's (idle) pilot jet's tiny metering hole will be gummed up solid. It is removable externally and so is the idle mixture adjusting screw. It's best to remove the carb and very carefully clean it. Gumout spray Carb Clean, at WalMart, AutoZone etc is the best stuff. The pilot jet meters idle speed and low throttle opening fuel, it's fuel flow trailing off with heavier throttle, overlapping the main jet's beginning range of progressively greater metered fuel flow. The pilot jet has a very tiny hole needing a very tiny fine wire and patient gentle cleaning. If you saved it, the yellow "No Oil" tag the Genny came with has exactly the fine cleaning wire you need. You must NOT increase the hole size with aggressive cleaning, or your unit will run rich, carbon up the combustion chamber and waste fuel. The control motor's power wire is long enough to remove and clean the carb while still connected. Removing the pilot jet from the top of the carb may require screwing in the idle stop screw to get it out of the way, so count the half turns you give it until it's away. The plastic capped pilot adjuster screw also has to be removed to clean out the needle and it's metering passageway. Remove the plastic cap, screw in the brass adjuster screw, counting the turns exactly, so it can be returned to there after cleaning. If you are not confident

you can do this job, find someone that can, as you can do expensive, system down damage without realizing it.

It is also very possible the fuel pump itself is so gummed up it will not pump. It uses the pulsating crankcase air pressure changes generated by the underside of the piston as it goes up-n-down. That's why 1 of the 3 hoses connects to the engine crankcase. A very clever, reliable and inexpensive way to pump gasoline, with zero parasitic power drain, from a fueltank that's at the same height or lower than the carb. It's internal diaphragm and 2 check valves all have to be able to "flutter" freely, or no pumping will occur. You can remove the pulse air hose from the pump and add your own cleaner one to the air port on the pump, allowing you to operate the pump by rapidly alternating mouth vacuum/pressure on your hose.
The purchase of a big bottle of Stabil brand fuel stabilizer would be a really smart one to protect it in the future. It uses so little gasoline and most generators usually have frequent periods of inactivity. Ethanol in gasoline also accelerates the corrosion and gumming up processes but the Stabil will protect you up to 2 years without damage.
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Only one who can see the invisible
can do the impossible.