Battery light won't shut off

You need to check and see if it's charging. My guess is it has a bad alternator and it wasn't charging and that is what killed the battery. Take it to an o'reilly's or an autozone and they can check the charging system for no charge. If it needs an alternator you can buy it from them and put it in yourself or if you don't have the skills to do it i would take it to a shop that has a good reputation and have them do the work. Don't bring the part to them. If you get a bad part or if the part fails you will have to pay labor again. Shops can get the labor covered from their supplier and they won't charge you again if it's under warranty. I would go to a napa authorized repair shop it gives you a 12 month 12,000 mile nationwide warranty.