Yep, quite possibly a crank sensor problem, either with sensor or associated wiring. Auto electrician required. Could also be things like Ecu fault or an earthing fault or a fuel pump fault. First is crank sensor to check.
Thanks for the replies, my copy of the 'Fiat workshop manual' confirms your suggestions (I was not checking! I'm looking for the ecu). The manual states that the ecu is found beneath the glove compartment - but! it isn't there (unless it is under the carpet)