Thanks to your responses, after hours of searching for the problem, I finally found it.
These circuits are run off of a subpanel so checking for a short between nuetral and ground was easy. I just disconnected the ground and neutral runs back to the main panel and measured the ground/neutral resistance. No shorts. Then I wired all of the grounds together in the box that was previously causing the AFCI to trip. No problems. The breaker did not trip. But it had before, when there were no walls and absolutely nothing on any of the circuits. Except one piece of equipment - an old radio that I was using. Sure enough, I plugged it in and the AFCI tripped. Turns out it has a ground fault.
Thanks for the help.
