Did give me the impression it was something like this (though had absolutely no clue what). Just taken it to the garage to have a Summit brace fitted & new pads and it started normally.
If you have a nosey on my350z.com or 350z-tech.com you'll find oodles of threads about Crank Position Sensor.
Battery will normally give some warning if it was that. With the Crank Sensor, when you unlock and put the key in the ignition, it just doesn't "crank", give it 30 secs or so, and it usually does. I normally flick the alarm the second time I try.
ps. With mine it wasn't the alarm that causes the problem as it did it the first time, the morning the alarm was due to go in, almost 5 years on, it does it occasionally, it is annoying but not keen to put Z anywhere near a dealer if I can help it.