Some of our cars do suffer the "crank position sensor" problem. Is a right pain, with most I've seen it's only periodically and when it does will do it a few times, then not do it again for ages.
If you crank it once, doesn't go, then switch off, flick alarm, then retry but give it a 30 seconds before you retry.
One thing though with the Crank Position Sensor, engine check light, ESP/TCS don't flash on any of the 350's I've seen here when it happens. So your problem might be something completely different.
Get a code reader on it before doing a reset. Good luck.