Q: Battery keeps dying and is corroded. Is it the alternator or the battery?

The corrosion may have an impact on how well the battery connection transfers the charge from the alternator. It is also possible that you may have a faulty alternator or a weak battery that is not able to take a charge. As you may know, the alternator is responsible for charging the battery while the engine runs by generating amperage and recharging the battery while the engine turns the alternator. The voltage regulator is a unit that regulates the charging of the battery by the alternator and maintaining a certain amperage while the engine runs. When the alternator is not working properly, this may result in the battery quickly losing charge and the car losing all power as you have described. I would recommend having an expert from YourMechanic come to your location to diagnose and repair your charging system.