I'll answer my question. Apparently the battery was bad. It only showed 100 cycles, and the status was normal, but it showed that it wasn't charging and would die if I unplugged the power adapter. After rebuilding the computer several times, I went out on a limb and purchased a cheap battery off of Amazon. That battery worked immediately and is charging normally. I don't know if I somehow damaged the original battery when I first opened the computer, but the problem was definitely a bad battery.