generator quits running
Seeing that it runs from spraying starting fluid directly into the carburetor this means that the ignition system is producing a spark and the compression system is moving the piston. Process of elimination shows that no fuel is reaching the carburetor (when you stop spraying fluid into carb the engine stops running. I would check the carburetor again. You didn't say if there was gas in the tank for three years, but fuel gets stale after a month. If left in the engine the fuel starts crystallizing and becomes less viscous (less fluid-like). The small orifices that the gas is moved through become blocked. Before a carb rebuild check on line to price a new one. Depending on the type and seller it may be easier and less expensive to buy a new one. To repair a clogged or dirty carburetor you will need to: purchase an appropriate rebuild kit,  remove it, disassemble it (separate plastic parts) and let the parts soak in a cleaning solution. Than its best to use compressed air to force air into any port and opening you see. Reassemble using the new parts from the rebuild kit.