99.5 Jetta starts, but stalls within 10 minutes

So, I recently bought a 99.5 Jetta. (99 with a 00 body), fixes a few things. Alternator, oil pan, head gasket. I recently drove the car just up the road, drove it back. Went to pull in to my spot and it shut off! Wouldn't start but would crank over. Days go by, same problem. Runs for about 10 minutes then just dies. Fuel pump works, fuel filter isn't clogged. And the fuel relay works. I'm out of suggestions. Anyone know anything about German engineering and willing to give me a little advice on what to do?
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