Sounds like it's too lean, hence the need for putting fuel right in the motor. You might need to adjust the idle mixture, which you might not realize even exists. It's the small screw which sits flush in the middle of the carb barrel, just under the little arm (still on the carb barrel) that the servo rod attaches to.

It might also be that your glowplug is shot, and it takes 3s for the glowstarter to get vibrated off the plug so then it dies.

Check your fuel lines, you might have a hairline split in them, or a blockage. Watch for air bubbles in the fuel line to the carb - there basically shouldn't be any (some will be inevitable as the fuel gets shook up)