I installed a new battery & not being a mechanic,I inadvertently hooked it up backwards. After I hooked it up the right way, I started the truck & it ran fine. But, the alternator light was on. I took it to my local Advance Auto & they tested it & said the alternator was shot. I bought a new rebuilt alternator & it still wouldn't charge. I had them test it again and they said the new one was no good & gave me another. We've installed the new one with the same results.
One last thing, when I hooked the battery up wrong, there was a small puff of smoke from somewhere underneath the battery. There doesn't seem to be anything under there except the steering column & there is nothing that looks like it may have gotten hot enough to smoke.

 

There's a splice there, including the fusible links. Also, the regulator for the alternator is in the ECU; that may have been damaged also.

For the former, a copy of the factory service manual (I believe it's in the FAQ2 sticky; try the FAQ1 if it's not) to double-check the wiring would be helplful; for the latter, the easy way is to replace the ECU and empty your wallet *grins* the more practical for most is to change to the external regulator; ideally with the resistor to replace the coil so the ECU doesn't fault.

RwP