2000 Jeep grand Cherokee will start then turn off

when I insert the key to start the jeep, it the engine will start and run for about 5 seconds and then just shut down. Sometimes this happens over and over again. Sometimes ten times before the jeep will start and stay running. Some days the jeep will start on the first crank. On the dash, there is a light that remains lit. It is a light of key with a circle and line thru it. I took the jeep to a dealer and had the key re programmed. When I picked the vehicle up, it started right up and the light was out. The jeep ran great the rest of the day and thought, Great PROBLEM SOLVED!! Until the next day, when I went to start the jeep and the problem is NOT fixed and the light is back on. I was told to get a new key, OR it could be the ignition switch, OR it can be the screen module?? Not sure what to do and dont have a ton of money to keep taking shots in the dark. Please help.