Have the Alternator Checked Out by a Local Shop. Have them put an Alternator Testing Machine on your Car, and see what they say.
Check your Battery Terminals for Corrosion. Replace your Battery, if the Corrosion has covered the Terminal. Use a Wire-Brush on the Terminal, and Remove the Positive Cabel from the Battery if you can.
If it's Rusted/Corroded bad enough that it's Stuck, then you Really Need a New Battery!!
Use some Pliers if this Happens, and Do Not Round the Nut off!!