oh also, to add to the things to check.. make sure the fuel can get back to the tank easy. the return should be resistance free. make sure any return pipes are not kinked or blocked.
you can test this by disconnecting the fuel return pipe somewhere in the engine bay where theres a connection, sticking the throttle body side into a empty fuel can and see if the engine runs normally. if this is the case it will a fuel pressure build up caused by something on the return line.
another way you can do is if you find a place in the engine bay where you can pull off the return fuel line see if you can blow through it. get someone else to listening down the fuel tank filler (i hope you have low fuel), they should be able to hear the remaining fuel thats in the pipe being pushed back to the tank then the air you are blowing down the pipe.
theres the possibility that it could also be the fuel pressure regulator thats built into the throttle body,it could be stuck closed. it could even be an issue with the fuel injector its self. i think someone on another part of the fiat fourm had a fault just like this.. injecting way too much fuel. i think it was a cinquecento.
the fuel pressure these cars run at is usually around or just under the 2 BAR mark. if its higher it usually means a fault of one of the above.
the in tank fuel pumps of fiats around this age are capable of producing pressures up to almost 10 BAR before they start to sag and stall so they can easy over pressure the injector should a blockage happen on the return line.
i still say that it could be something electrical... but you cant rule out the mechanical side as the regulator is purely mechanical.
if you do find the problem, please do post the results. it will help someone in the future with the same issue!