My son has a 97 Jetta with 213,000 miles on it. It will start up, though roughly, but then die out in 8-10 seconds. The module (coil) has been replaced, the plugs and wires replaced, and the fuel filter replaced. Right after the filter was replaced it ran for a bit, maybe 5 miles, then it backfired a lot and has started back with the same problem of not staying running. The fuel filter was really full of junk, so we added dry gas and fuel injector cleaner.

We're running out of ideas. Any thoughts?

maybe you got some junk in the fuel line that went into the injector and clogged them. You might have to remove the injectors and manually clean them with brake cleaner.