Been a while since I've fiddled with carbs... First thing that comes to mind is the accelerator pump....if you (or someone) steps on the gas (engine cold and not running), can you hear/see gas squirting in there? If it's just a dribble, try pumping like 10 times and then see if it starts. If it starts, then the culprit would seem to be the accel. pump.
I'm thinking that's a solex, and from what I remember, they like to have vacuum leaks...tightening all of the screws a little may help. Keep the fuel lines away from heat...just in case the stalling is a flirtation with vapor lock.

With some luck, some carb experts can chime in, and add more info/help.

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09 Jetta TDI
1985 300D