Starting, running and then dying immediately afterwards is a telltale sign of weak fueling. If you got a pressure tester (make sure it's rated for fuel injection), it's quite easy to test just as long as you've got a shrader valve port thingy on the driver's side fuel rail. Spark plugs don't like to sit, so you might also check them as well.
In the case of a fuel-injected engine, this same problem can also be caused by a faulty IAC valve. The pintle can get fouled over time and stick shut which will choke and kill the engine at idle. This can be detected by trying to start the engine with just a little throttle input. If the engine starts and stays running while doing this but dies when you let off, a faulty IAC is likely the problem.
