Autopilot update:

Well it turns out that the autopilot's computer is fine after all. That means that the problem is likely related to the wiring, and may be as simple as a bad fuse or loose connection. That's pretty good news, really! Now I just have to reinstall the computer and chase the ghost that keeps the unit from working. Doesn't sound like a lot of fun, but at least it isn't going to cost us a ton of money.