If you know anyone who has a Snap on MODIS or anything similar, you can view live data from sensors.
Typically, if a crank or cam sensor are bad, you won't have a minute of running fine then chaos. Most of the time the car won't run at all due to the fact that cam and crank sensors perform such a critical function.
Does it run fine until it warms up, or just for the first few seconds / minute? If it runs okay until it gets close to warm operating temperature, my guess would be that it's a sensor of sorts, but most likely not the cam or crank sensor.
When the car is not fully warmed up, the ECU runs in closed loop mode. Math people and programmers are not creative when naming things. Closed loop mode is exactly that; the ECU does not read non-critical sensors, instead it uses preassigned parameters to manage the engine. For example, instead of reading manifold pressure and exhaust gas composition, predetermined values are used in place of MAP sensor and oxygen sensor readings. Closed loop operation is very "baseline" - and very safe. It ensures an air fuel ratio that is rich to prevent damaging lean conditions.
Once the vehicle approaches warm operating temperature, the ECU switches into open loop mode, where it considers input from all sensors to manage the engine in such a way that it operates with maximum efficiency given the external conditions.
Most typically, when a crankshaft sensor goes bad, the ECU has no frame of reference regarding when to ignite the air / fuel mixture in the cylinders. The crankshaft sensor is not subject to open / closed loop operation. The ECU consistently reads crank position regardless of operating mode. The same applies to the camshaft sensor.
