Will not stay running

Can I ask if the security light is flashing? If so this will cause the engine to start and then just shut off like you have described. I would do a hard system reboot, remove the negative battery cable and hold it to the positive post for 1 minute then reconnect. This will discharge all capacitors so the system can come back online. This guide can help as well:

https://www.2carpros.com/articles/how-to-reset-a-security-system

If not this is common when you have a vacuum leak or the throttle bore needs to be serviced. here are three guides to go over when fixing the problem:

https://www.2carpros.com/articles/throttle-actuator-service

and

https://www.2carpros.com/articles/stall-at-idle

and

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

Please run down these guides and report back.