How many times does the FI light flash so we can determine the fault code? A fault code 1 with engine cutting out can indicate a failing MAP sensor.
If it isn't a fault code 1 then you could be lucky to just have a bad oxygen sensor. I don't remember the code for that and I have to go out now, one of the guys here will probably get back on this soon.
Put the side stand down and start the engine, do not touch the throttle. If there is a code stored it will flash. long flashes = 10 , short flashes = single digits. Get back to us with the code. If no code is flashed check your battery connections.