Ok, so you're saying you temporarily (for a minute) connected the battery in backwards. You realized your mistake and swapped them around. It drove fine for 3 days and now the battery is dead? Is that right?
An alternator has diodes in it as it produces alternating current which must then be converted to DC voltage for use in the car. It could be that these diodes have failed or that the alternator itself is now reverse-polarized (I don't know how the windings between a generator and alternator differ), so you basically have no charging system. A new battery would work, but would also go flat in a few days. You can check that with a meter, of course, verifying the output voltage from the alternator. Back in the day, people would actually take apart alternators/generators to swap out the diodes, brushes, and the bearings to re-new their alternators.
I'm one of those people who used to take alternators and generators and voltage regulators apart to fix them.
I can assure you - due to the basic differences in how an alternator and a generator work (one has permanent field magnets, one doesn't, one has a segmented commutator the other doesn't) that an alternator will never put out reverse polarity.
It may however put out a voltage that measures OK with a voltmeter, but has no current behind it (limiting charging) or DC voltage with a high percentage of AC ripple on it (caused by shorted diodes - the clue for that is the diodes often "sing" - make a singing sort of noise 'zzzzzzzzzz' when shorted.) And sometimes both happen at the same time.
The battery in the car works like a great big capacitor and helps to dampen the AC ripple. It's enough with a healthy battery/alternator that the ripple isn't an issue. If the diodes are shorted, or the battery is weak - enough ripple can get through to disable some devices and perhaps destroy other devices.
Part of what causes electronic device failures after a battery reverse connection is the sparking that occurs as you connect the battery and then in a panic disconnect it. That sparking causes high-voltage spikes to travel through the entire electrical system of the car, causing damage that may not immediately show up (eventual solid-state-device failures - used by "T" failures of the device substrate.) They might show up hours, days or even weeks later.
That's also the reason that in general - jump-starting of any modern car isn't recommended or suggested by the vehicle manufacturers. They typically call for charging the battery, sometimes with the positive lead from the electrical system disconnected. It's not JUST the reverse connection that causes the issue (as I mentioned - that's pretty simple to protect against) - but it's the high-voltage spikes. That's harder to protect against (think surge-protectors, typically once they see a surge the protection is now no longer active - the device sacrifices itself to protect the other devices that are connected to it.)
I believe what he said was - he reversed the battery connection, disconnected it, reconnected it correctly and the car ran. Now after 3 days it no longer runs despite installing a new battery. I think he also made mention of the fans running as soon as he hooks up a battery to the car.
The hardest thing for me, would be to try to avoid guessing, and acting on a guess. I always guess wrong and waste time. Instead, figure out someway to find the smoking gun. I’m sure this is already stuff you’ve thought of.
David made a very astutue comment here.. guessing gets expensive since the
last part you change will be the defective one - but you might change a
LOT of other parts getting there. Hence my suggestion (strong suggestion) of getting it hooked up to a diagnostics tool.
Or take it to a dealer who I'm certain is no stranger to this issue.