Bad Battery or Bad Alternator?

Okay. My little 96 Ford Escort has been running fine. However, tonight after work, with the car sitting in the parking lot at my jobsite for 8 hours, the car started up no problem. I drive about 2 miles to a convenience store, go in the store for like 2 minutes, come back out, and try to start the car… It's TOTALLY dead. Radio won't even come on.

So, get it jumped, it starts right up after connecting the jumper cables. Drive 20 miles to my home, no problems, and as soon as I get home. I turn the ignition off… And immediately try to start the engine again. Nope. Dead. Radio won't even come on again!

Just seems weird that this car has went from running and starting perfectly fine to this "totally dead" crap so quickly.

So. What are the odds here? I know I can have the battery and alternator tested. But let's see who is right and wrong. What is MOST LIKELY the problem?

Have you checked your battery terminals? Sounds like they are dirty.

Loose battery terminals or failing solenoid contacts if you have a Denso gear reduction starter.

Sounds like a major battery failure. While the engine is running the alternator was keeping everything alive, but as soon as the engine stopped the alternator power was gone.

Check that the battery terminals are fastened on tightly, and check that the lead where the negative battery terminal attaches to the car body is okay.

If the battery is faulty, don't jump start the car and run it. The alternator can go over voltage without a proper battery to limit the voltage range, and you could burn out bulbs and the radio.

Whip the battery out and take it to a car battery dealer and get them to check it. If it has a fault, you know what is needed. If they load test it and it seems okay, then you need to get the rest of the car's electrics checked.

From what you have said, I believe the alternator is fine.

Twenty miles of driving should charge a battery unless it's so far gone it won't take a charge. I doubt it's the alternator. If the alternator was bad you wouldn't have driven very far on a dead battery. The alternator does NOT supply power for the car. Its purpose is to charge the battery which supplies power for the car. If the battery is more than 4 years old, it's probably the battery.

Jump your car again and while the engine running disconnect the battery from the car and if the car turns off then the alternator is going bad. If it stays on then the battery is dead and the alternator is not charging the battery. Check the wire on the alternator that connects to the battery and make sure that it is not covered in battery acid. Also check the terminals of the battery and make sure there's no battery acid on it. One other thing you can check is the water inside the battery. Look in it the water should be up to the edge of the hole. You can fill it up with tap water.

Bad connection somewhere.

Sounds like a battery issue. Start the car and run a test with a multimeter and check the volts, should be 13.6-14.6. I would have the battery tested

Get a multimeter. Get a jump again and with the engine running, measure the voltage across the battery. 13.5 volts to15 volts, the alternator is good and the battery has a dead short and will not receive a charge.

Do not disconnect a battery cable while the engine is running to test the alternator. You can fry the alternator and the PCM/ECU.

Te car is 20 years old, and the battery may be quite old as well!
However, when you drove into the store did you go over an abrupt bump?
the bump, may have shifted the battery sediment, into a pile, that touched the plates, and shorted the battery.
a new battery would be a wise move!

How I can have?

Something is disconnected. Like corrosion on a battery post. Or something in the battery broke.