Battery light

Are you sure the new alternator is good? That battery light shouldn't be on. Should measure 14.7 volts when running. maybe there's a fuseable link burned out in the wiring somewhere, maybe near the battery? Are the battery terminals clean and in good condition? Also check where the negative cable goes to ground, either the frame or the engine. A bad ground can cause alll kinds of weird problems. On my 2002, the negative cable has a short wire to the chassis right by the battery, but the main cable goes behind the engine where you can't get at it. That is the main ground that I'm wondering abourt. You could put a jumper cable between the neg. batery post and the engine block, to test that. Most likely, that's not it, though. I'd be more suspicions of that short chassis ground comming right off the battery. Disconnect it and clean and scrape, and put it back.

Check for 12 volts at the alternator large wire with engine off. If there is no 12 volts then the fusible link to the alternator wire is open and in need of repair.