Volkswagen Repair: 92 GLI 16V stalls, wont restart, psi minimum, differential pressure

Question
My 92 GLI 16V stalled on the way home from work the other day, after about 3 minutes of driving. It would crank, but wouldn't restart. I let is sit for about two hours, and it started again, and ran for about two minutes, then died suddenly again. I replaced the transfer pump, but no change. I did get it to start one time, and held the throttle at about 3K RPM, and it ran, but not well; when I let my foot off the throttle, it died again.
Does any of this sound familiar? What should I replace, or test, the differential pressure regulator, or the main fuel pump? Any help is appreciated...

Answer
If you have the tools, test the fuel pressure under the hood, at the rail to see if you have enough pressure to run the engine.  35 psi minimum...should be more like 45 to 60.  I'm thinking you are on the right track though.  Without being able to get my hands on the car to test myself, I'd have to say that the fuel pump is a highly probable choice.  It's nestled into the body of the car almost in the middle, a little over to the right(passenger side), and I would highly recommend changing the fuel filter at the same time...oh, yeah unless you've got uniforms, and laundry service wear old clothes that can be thrown away afterwards.  There is going to be gasoline all over the place, you included...so NO SMOKING!!!!  Be prepared to fight with the fittings, and the hoses, and don't try to reuse the clamps.  Get under the car first, and put a complete list of parts together from pump to filter to clamps, and if you have a digital camera take a picture or two so everything goes back in the available space.  I seem to recall a "U" shaped piece of hose, some brackets on just about everything, and clamps that misbehaved on the last one I did that was nearly identical to the GLI...an 8V GTI, but very similar, overall.  I guess if there are still runability issues after that, start looking for the tell tale cracked or broken vacuum hose(s), under the hood.  Sounds to me like your daily driver though, and you probably know more about this car than I do.  Transfer pump is low pressure, and fuel pump is high pressure...
Anyway, I agree with you, Neil.
I neglected to say it's right above the rear axle, but you knew that already.  Good luck.