How long after a radiation exposure do victims start experiencing symptoms of radiation poisoning and begin to die?

Depends: "radiation" is not just one thing or one entity. There are different types of radiation with different routes of exposure, and health effects depend on several things such as the type of radiation, the strength of the radiation, the route of exposure, the proximity to the radiation source, the health status of the person exposed, etc. See http://en.Wikipedia.Org/wiki/acute_radiation_syndrome.