1993 Other Jeep Models jeep will not stay running more than

I have a '93 Jeep Grand Cherokee with over 326,000 miles. I am having difficulties getting it to run more than about 15 seconds. It cranks easily but after the 15 seconds it will shut off and the lights will start blinking showing me that this should be a security system issue. I changed the battery out as I have on previous times but I have not gotten any results. I can crank the Jeep repeatedly and it will start right up, but it refuses to stay going.