Join Date: Aug 2018
Location: Lowell area, MA
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Welcome to the forum! (from another recent newcomer)
Which 2000W Honda? The red EU2000i inverter unit?
If so, I have one of those. Mine needed partial choke to run smoothly, when I bought it. I cleaned the carb in an ultrasonic cleaner, and it ran great after that. These engines have a fuel pump. It's possible that your fuel pump could be having trouble, though I'm not sure if that would give these symptoms. A somehow-still-dirty carb seems like perhaps a more likely cause.
Will it run for a while on full choke? Like several minutes, for instance?
It's possible you could have an intake air leak, such as around the body of the carb, where it mounts to the engine. One way to test is to spray something flammable (like carb cleaner) around where the carb meets the engine, while running. If the engine sound suddenly changes, then you have a leak there, and stuff is being drawn into the engine. An air leak can make the engine run extra-lean, which adding choke would help counteract.
Though, note that the EU2000i uses an electric-motor driven throttle. So spraying liquid (like carb cleaner) on that little motor is probably not a great idea. I've heard of people using an unlit propane torch, and cracking the torch's valve open, to provide a flammable gas, and moving the torch tip around the engine, to listen for the engine sound changes that indicate you're drawing that fuel into a leak. Obviously, this sort of test needs to be done carefully, and preferably quickly, as you don't want to be providing a lot of unburned flammable gas around a running engine.