2002 Impala 3.8 will not start. Nothing happens when using the ignition switch. Can jump start the car by jumping through the crank / start relay and with the ignition switch on and it starts, but the engine shuts back off in seconds. (starter checks good and replaced the crank relay)

You need to check and see if the security light is on or flashing.If it is then the security system is what is keeping the vehicle from starting.You need to get the codes from the Theft Deterrent module and from there it will need to be diagnosed to find the problem.The Theft Deterrent module and the PCM is what allow power to the starter once it sees that the correct key has been used.If you have a worn out key this could cause it not to work.So if you have a second key you can try that first.If the light is not on or flashing then you have to check the crank fuse on the left side of the instrument panel.Let me know what you find out.I`ll be glad to help you out with any codes and tell you what they are.Good luck.

Check the 10 amp PCM/BCM relay fuse inside the car. If that isn't it, please get back to me, and tell me again how you got it to start--how did you jump the relay?