Extremely high failure rate on reman alternators. Is the charge light on? Does it light up when you first turn the key when trying to start with a full charged battery?
The charge light MUST light up or the alternator will not charge. It's part of the circuit that excites the magnetic field in the alternator.
A voltmeter costs $10. Buy one and grab a shop manual to diagnose instead of throwing parts at it.
The alternator is not charging the battery. Running a car on the battery only and you will have power for about 4 hours. Think how long before your headlights go dead if you leave them on with the car not running. The starter has no connection to this problem so I don't now why you replaced it. Most likely since you have replaced the alternator it is the voltage regulator that has failed. There are three types two are mounted inside the engine compartment and the wiring from the alternator to the battery is connected. Some alternators have the regulator built into them. I have no idea what type you have You can test the regulator by running the engine. (recharge the battery with car battery charger) then use a volt meter to check the output from the regulator to the battery. It should be about 14 volts.
Sounds to me like it is in the brain box(Computer)(CPU).
More than likely you have a sensor that has gone bad and when the cars engine gets hot enough it causes the sensor to go out.
Try letting it set and cool and if it tries to turn over than it will give you a bit more insight.
Take the car to auto zone or O'Rilleys(if you can get it there)and have them hook it to their diagnostic tool.
This will tell you what if any thing is wrong with the cars sensors,computers, relays, and well just about any thing to do with your cars electrical workings.
Hope this helps. Good Luck and no not stupid at all to invest money into your car. without 1 you can't do anything
The alternator and voltage regulator are usually replaced as a pair. This is because a bad voltage regulator can possibly damage a new alternator, and because a bad alternator can possibly damage a new voltage regulator.
I suspect that your car is new enough to have the voltage regulator built into the alternator (contact a car parts store to verify this). If so, you already have replaced them as a pair. Most certainly the voltage regulator can cause the problem that you see. A volt meter could tell you how much the battery is charging. (It should be 13 volts when the car is off, and it should be about 14 to 16 volts when charging). You can check the specifications (the correct charging voltage) for your car at the dealer (Ford dealer). Or, you can get a motor manual from the library.
Your problem is that the battery is not being charged. It runs for a while on the stored energy of the battery, and, once that is used up, the car stalls.
It is also possible that the wiring to the alternator (usually called the pigtail) has a broken or incorrectly connected wire.
I don't think that the "brain box" (aka electronic ignition module) is the cause of the problem.
I think that it is an excellent suggestion to take it to a mechanic (or car parts store) to have them diagnose the problem. It is often too expensive to keep replacing parts until you eventually find the problem. It is better to diagnose the problem, then fix only what you need to fix. On the other hand, your car is quite old, and many of those things that you replaced likely needed replacement anyway to assure that the car won't break down from old age.
97 ford taurus brand new starter alternator and battery. Car wouldn't do anything so we changed the starter and it worked for about 4 hours then lost power while driving. Took battery out and charged it and took out alternator tested it and it was bad so replaced it. Same thing, ran about 4 hours and died while driving. The battery was actually too small for the car so we thought alternator killed a cell, so bought the right kind of battery and replaced it, same thing? 4 hours and while driving lights go out, starts sputtering and dies. It tries cranking a bit but after cranking a bit it stops and won't crank at all. We hear fuel pump working and all the fuses look in good to decent shape. Battery connectors are clean no corrosion, alternator wire are clean too. Where could the problem lie?! We've sunk literally our entire paychecks in 2 days fixing all the parts that seem to be the problem (stupd I know) but somewhere something is going wrong. Help!!! It's our only car for 2 more weeks...