All the symptoms of a bad fuel pump, if you have a fuel pressure gauge there is a schrader test port on top of the engine, it should be a steady 58psi.
+1 and I'll add that the 58psi needs to be with the engine running. With the ignition on but engine off, the pump runs for a few seconds and may appear to come up to pressure but with the engine running and a dodgy pump it can't maintain the pressure hence the cutting out.
Have been there, and have just bought another pump as a spare.
