Here is the update. The problem all along was a bad battery - go figure. I was reading through some troubleshooting tips on a different post, and decided to try some of the tips. Everything pointed to a bad battery. Found a loose connection on the positive terminal. So, I replaced that, put in the battery out of my other truck and she started right up.

Still think the alternator might be part of the problem. Headlights seem pretty dim until I hit the gas.