Why will my battery light not stay off?

@pamelaeleam this sounds so much like an alternator issue. Do this. Get a voltmeter and with your car off check the voltage on your battery. You know, Voltmeter to DC V at a range of about 30V or thereablet (depends on your meter). Then black probe to negative post and red probe to positive post. Let us know what you get. A good battery has usually up to 12.6V and a reading below 12V is usually a sign of a bad battery. WE know your battery is new but discharging, so your voltage may be lower, which for now is okay.

Now, do the same thing but start your car. Your voltmeter should now show 13.6V to 14.4V. If it does not, your battery is not being charged.

Check the wiring on the battery post and the battery clamps. Make sure they are not corroded. Check the wires coming from the alternator to make sure they are properly tightened and not corroded. OF course, do that while your car is turned off.

Let me see if we can find a wiring diagram to see if there is anything in between that may have failed and thus does not allow your battery to charge. If you find anything that looks odd or doubtful, it is okay to take some pictures of it and post those on here with your question. 在已经存在的问题里加入图片

Okay, so here are the 2006 2013 Chevrolet Impala Wiring diagrams for your Impala. Here is the charging diagram.

There are two fuses that are of interest. One is a fusible link between your alternator, starter and then the battery; one is the fuse for the BCM. That is the fuse in the fuse box which is "mounted to the right strut tower". Check those for continuity.