Hi,
Have you got red & green L.E.D.'s in the rear view mirror?
Are these both working?
As one of these being blown can cause the symptons you are describing, though i have never heard of the car cutting out once the car has been started.
Have you replaced the fob batteries? even if the fob is still opening the car ok replace them with new.
Have you tried your spare key fob?
is there anyway i could find a step guide on how to do this online?