Bertone starts, then quits. Any suggestions?

I have a 1995 Bertone that's in pretty good shape, considering that it sat for about 6 years. After I bought it, I changed the fluids, put a new battery in it and tried to start it. To my amazement, it started right up and ran great for about 10 seconds! Then it just died. But not right away, instead, it kind-of faded out and quit. It would start again, but the same result. I have tested the fuel pressure and that's okay. I don't think it's the ignition system or injectors because it runs great for about 10 seconds. It might be the engine computer, but why would it even run if that was not working? I even see the oil pressure light go out before it quits, so I think the pump is producing proper pressure.
Any ideas? It's sad to not be able to drive this really cool car!
Thank you for any suggestions or even a referral to experts to talk with.
email: jjakek@aol.com

when you say you have tested the fuel pressure do you mean you stuck a gauge on the fuel rail and watched the pressure before, during and after the cut out? if not, that is what you need to do. it sounds like the fuel pump is building up pressure ok for starting but is unable to maintain pressure, possilby due to a faulty pump, blocked filter or a weak or damaged pressure regulator. after sitting for 6 years the pressure regulator would be first on my list, it has a rubber diaphragm inside that often perishes after a very long period of not getting used. this causes overfueling, and the engine appears to choke. the reason this does not happen on initial start up is the fuel pump only primes for a few secs. once started it then takes a fre secs for the pressure to raise so much that overfueling kills the engine. have you checked for wet sparkplugs after the cut out? thats usually a good sign that the pressure regulator has failed.

by the way, i'm not sure what a 1995 bertone is? there are several fiat models that were styled by bentone, but none i can think of that were made in 1995 except a punto cabriolet. i know many people in the states call the fiat X1/9 a bertone so i assume you mean a x1/9, but it must be earlier than 1995.

6 year old petrol won't do you any favours.