Car wont stay started

Try and scan the computer for codes. If the vehicle starts up okay and then shuts off after two seconds then you could have an immobilizer issue? If that is the case if you have another key then try using that key instead. For now here is a link to help you scan your cars computer if you have a scanner.

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Okay, it sounds like the pump is getting the prime signal but then the pump relay is shutting off. Usually this is because the ECM is not getting a signal from the crank sensor telling it that the engine is running and it shuts off the fuel because it cannot determine a timing signal without the crank sensor input. You could jump the pump relay to see if it stays running, but you would need a scope or scan tool to verify that the crank sensor has failed. Or as this is a common sensor failure just replace the sensor and the problem should go away.