I would recommend replacing the fuel filter. Fuel filter is just that, filters out dust, dirt, etc... from the gas tank. So since you had the fuel pump replaced, and with that many miles on the car, and had some issues with the fuel system before... it's a pretty easy, low cost, simple to replace item.
So unless your 2004 Golf is very different than my 2004 Golf GLS (Automitic, Gas, 2.0L 4-cyl), it 's an easy item to replace. They only cost about $20, filter is located at the rear of the car, in front of the passenger side rear wheel.
https://www.2carpros.com/makes/volkswagen/golf
And if you don't want to do it yourself, just about all quick service 'Oil Change' places will do it next time you have the oil changed.
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Friday, November 27th, 2009 AT 2:57 PM