durango theft system shutting off engine

My cousin has a 2001 durango that starts and runs for about 10 seconds and then shuts off. I assume that the cars theft system is shutting it off. She has 2 different keys and it does the same with both keys so I think it must be the sensor or the computer not recognizing the key as the correct key. It does not always do this though,only intermittently. How can you tell if it is the sensor or the computer. If I get a different sensor do I need the keys from the same vehicle , and the same goes for the computer. How similar must the donor vehicle be? model, year, engine,options etc?

so theres a red flashing light in the cluster\

the security light flashes sometimes but not every time