From the symptoms you describe I'g be heading straight to the jets. Main and idle circuit.If it sat for that many years the jets will have healed up from a combination of fuel residue and corrosion.you obviously have compression and spark from the fact that it fires up on a direct prime of raw fuel in the cylinder. But it dies because the carby isn't supplying a continuous flow. If you're just planning to sell it you can try cleaning the jets, start with soft materials like a toothpick and even up to fuse wire or other copper wire. Using anything to hard can enlarge the jets and mess up the tune. If you plan to keep it, spring for a carby overhaul kit and replace all jets and seals.
Oh no carb cleaner will not put a dent in residue if it is old enough. Are your jets the kind that can be replaced? Also if you can get a wire through them that sometimes works.Please tell me you removed or replaced the inline fuel filter if there is one. Also there is often a screen or small filter at the base of the fuel tank that could be the issue.Pretty sure it is a fuel issue though, just a matter of working through all the possible issues at this point.