Died while running

If you haven't done it already you might have them run it for codes to see if it is showing any. Autozone does it for free too.

change the fuel filter and check the fuel pressure

I'm not sure if the Aurora is a special type of car that requires a different way of jumping, but when u jump start most cars, you place the red end of the jumper cables on the positive/ red side of the battery and the black end on the negative. You want to make sure the jumper clamps are touching the metal part of the battery post (so if there's covers on the battery posts, move them so the cables have good connection. The same procedure is used on both cars. Be careful not to touch the end of the cables together, as doing so will make them spark if one end is connected to the running vehicle. Let your car charge a minute then try to start. If it starts, let it charge for 5-10 minutes and run/ drive your car after disconnecting to make sure the battery does not die the next time you shut it off. If it does not start after a few minutes of charging, adjust the clamps to make sure they have a good connection, wait 2-5 minutes longer & try to start your car again. *It is normal to hear the car that is jumping you idle more quietly when your car starts pulling juice from the charged battery. Also, remove jumper cables after charging, making sure not to touch the ends togther- as it will spark again. *it is not necessary to shut off the car that's jumping you before attatching the cables, or after charging. If your car still doesn't start after repeatedly adjusting cables and trying other cables to see if it is the cables not working, you may need a new battery or alternator. I would have the battery tested to see if you need a new battery before considerring the altinator.

Might have to reset the codes on the computer. Take the + battery cable off the battery and reconnect it afer 5 minutes. Next try to start the engine without holding the gas petal down, it should start and run rought till the computer resets itself. If engine stops, restart the engine and hold the gas petal down and give it enought gas so it will run smooth, it may take 5 minutes or so for it to smooth out and run at idle speed. If this did not fix the problem, check for a vaccum hose that may be off some where on the engine

How is your oil pressure sender?? The fuel pump runs thru it after start. Watch the gauge while cranking It may give indication

remove dog house locate test port and install guage should be 45-60 psi

ok..you must have more than one car???? you don't drive the 300 atall im guessing. #1 start car drive up the road and \back to your house. #2 let it idle till problem starts. #3 once it does start with the problem keep it alive with the gas pedal. #4 once your have it safely from dying in higher rpms "rev it" like a kid would, you know like if you were gonna race some one lol. be careful not to over rev or damage engine. you should do this for five minutes no longer than that. #5 let it idle for another 5 minutes. #6 repeat every day until problem with idling decipates. it took mine 3 300e like 3 days of this. if your not going to drive the car once you get the problem out of the way. turn the car on everyday and let it idle for 5 minutes atleast and take it for a short drive once a week. they get lonelly you know lol. later on you can just turn the car on every 2 -3 days and let it idle but still take it on a short drive atleast once a week

Cam position sensor

sounds like it could be. does the headlights look dim while running? or does it die out while driving? or do you have to jumpstart it everytime?

It sounds like your fuel pump is going bad.