2003 ford Windstar starts but won't stay running. Changed fuel pump about 4 months ago and changed fuel filter this past weekend.

When you changed the fuel pump did you change the fuel filter? I changed mine in my expedition 3 months ago and also changed the filter. Reason to change is because a fuel pump usually fails because of a semi clogged filter. The pump has to pump a lot harder thus it burns out. First i would check to see if pump is running. Have someone turn the key on and listen with the gas cap off. If you hear the pump engage then it may be a clogged filter. If you dont hear the pump then it maybe your pump reset. My pump reset is located on the passenger side front seat just in front of the door. Plastic shield must be taken off. There is a red button that you need to depress to re engage the pump circuit. Once you depress then it should start. Check your manual for pump reset location. Good luck

please RUN the scanner/computer for easy diagnostic and fix it.
You can have faulty sensor+ignition coil +PCM+BCM+wires spark+etc.
see the diagram attached.
God bless you

change the fuel filter and check the fuel pressure

Either your battery has failed or the alternator/ regulator/rectifier has. With the engine running, check the DC voltage at the battery terminals it should be above 13 volts but below 15. If it is outside this range then your alternator or regulator has failed. This is the most likely. If it is in this range then you need a new battery. As you have changed the battery it may need changing again if the rectifier has failed. but hope it is the alternator giving no output.

have you tried the air-flow meter

Have the fuel; pump checked for pressure bleed down after sitting, it should hold pressure within 5 PSI of rated running pressure after shutting sown the engine for extended periods.

fuel pick-up in tank is blocked it has a sock over the end as a gross filter to keep out any big junk from getting sucked into the pump and causing damage to it. the sock can get so plugged up that no fuel will flow, causing the pump to run for a short time then with no fuel flow to cool it it trips the safety and shuts off

As with any no-start or stall problem you will need to figure out if it is a fuel or ignition issue.
The high idle usually means you have a vac leak or a problem with the throttle body or idle air control valve. The control valve is how the computer controls the idle speed.
You'll need to watch the fuel system and spark to see which is being affected when the engine dies.
You might want to hook a test light up to the coil to see if it is loosing voltage for example.

Probably the inertia switch for the fuel pump..You owners manual should show you where its located..See if the button has pop up ..If it has push it back down until it clicks..If it wont stay down then hold it down and see if it will start..If it does you will have to replace it..If thats all good then check the relay for the fuel pump..

You have two coils on this engine. Test each wire for spark with the engine running. You'll find at least one wire not sparking. replace the coil that has the wire that's not sparking.