Battery light will not go off

The battery light indicates there is still an active issue with the charging system. There will most likely be a code set in the PCM (Power-train Control Module) that will give us an idea where to go. Take a look at the article below regarding how to retrieve codes yourself with a simple handheld code scanner. Most auto parts stores will also provide this service free of charge.

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Let me know what you find!

I have done this also and nothing is showing up on the reading! Could it be the car’s computer?

That seems odd. This particular vehicle should typically set codes for charging system issues. Let's move on using a multi-meter and see if we can narrow down the issue. Take a look at the articles below to get started. The first discusses the use of a multi-meter if you're not already familiar. The second walking you through the process of testing the charging system. I've also attached a wiring diagram of the charging system for your reference.

Multi-meter instructions:
https://www.2carpros.com/articles/how-to-use-a-voltmeter

How to test an alternator:
https://www.2carpros.com/articles/how-to-check-a-car-alternator

Let me know what you come up with!