Electrical issue

Measure the battery voltage with an inexpensive digital voltmeter while the engine is running, then holler back.

Those two have to be the same. First, measure at the alternator's output terminal with the engine off. You should find full battery voltage there. If you don't, suspect a blown fuse in the under-hood fuse box. More likely you will find voltage but that doesn't mean much because a voltmeter doesn't draw much current so a poor connection won't show up. A poor connection WILL show up when high current is trying to get through such as when charging the battery when the engine is running.

For a 2002 model, I'm pretty sure you do have an alternator fuse bolted in the fuse box. With the engine running, measure the voltage at four places; each bolt that holds the fuse in, and each cable terminal under those bolts, (or nuts). You're looking for two adjacent points with different voltages, even as little as 0.1 volt. If you find any, that connection must be taken apart, cleaned, and tightened.

There has to be a place where you're dropping 1.5 volts between the alternator and the battery. I'd be willing to bet you find that bad connection and any other problems will clear up.