Cranks fine, but now the battery light stays on

Hello,

The battery light staying illuminated when the engine is running indicates that the battery is not being charged by the alternator. Which could be due to a bad alternator. It can also mean there is a wiring issue.
Make sure that the battery cable is secured and free of any corrosion.
Test the alternator output to the battery. It should have 13.6V to 15.2V, with the engine running.

Here is a helpful video of alternator testing:

https://youtu.be/Z-p4dMJUpUw

I have attached the alternator replacement procedure below.

Please let me know if you have any questions.
Thank you.