I no next to nothing on these cars (as with all cars if im honest ) Ive only owned my 350z for a few days, but just sounds very similar to when I first went to test drive one. I tried to start the car and it wouldnt go.
without depressing the clutch when kicking up the car (on my 350 anyway not sure about yours) it does the exact same thing as sounds like your saying here- some sort of imobliser type effect. all electrics work and car just whines, no turn over when trying to start the engine. could be some sort of electronic imobilisor (not sure if this is mispelled) problem. albeit unlikely and I cant think as to why it would cut out the car completely whilst driving?
For the lights etc to still work the connections should be sound on the battery.
For not even any attemp at tick over something starter related i would think not battery.