Not wanting to stay running

We need a lot more history and details than that. Does the engine stall while you are driving and will not restart until it cools down for an hour? Will it stay running as long as you hold the accelerator pedal down 1/4"? There is a half dozen different groups of symptoms that could apply to "will not stay running". Also, when you have an engine-related problem, please list which engine size you have. Was the battery recently disconnected or run dead?

No priming necessary. The fuel pump runs for one second each time you turn on the ignition switch. Also, once it ran out of gas, what was in the lines stopped moving, so there is very little air in them. What can happen though is the pump pulls gas out of a little bucket so that gas does not run away from the pick-up when the level is real low and you are going around a corner. Once you run out, you need to put in enough gas so it is high enough to overflow into that bucket. On my rusty trusty 1988 Grand Caravan, adding just a little gas was sufficient because the filler tube dumped it right into that bucket. Now I am driving a 1994 Grand Voyager, and with that one, gas from the filler tube misses the bucket. I have to put in five gallons to get the level high enough so it spills over into the bucket, then the engine will start.

Before you completely fill the gas tank, listen for the hum of the fuel pump for one second when you turn on the ignition switch. Instead, if you have a fuel pressure gauge, attach that to the fuel rail on the engine and see what you have for pressure. If you never hear the pump or if the fuel pressure stays at 0 psi, suspect the fuel pump is not working. You do not want to have the tank full if you need to pull the pump out.

Next, if you do have fuel pressure of around 45 - 50 psi, the engine should run if you hold the accelerator pedal down 1/4". If it does stay running, the cause of the stalling and/or failure to start is the idle speed is too low, and that is a result of the battery was recently disconnected or run dead. The Engine Computer needs to relearn "minimum throttle" before it will know when it must be in control of idle speed. To meet the conditions for that relearn to take place, drive at highway speed with the engine warmed up, then coast for at least seven seconds without touching the pedals.