Q&A

 Master

I would check that the battery connections are clean and secure. If they are corroded you can clean the connections with hot battery and baking soda. Ensure the battery is secure. After that check to see if electrical connections are clean and tight, battery ground cable is good. Perhaps the ignition switch electrical portion is failing. That type of problem used to happen Hondas when the ignition switch was failing but the head lights should work independently of the ignition switch.

 Rookie

If the system works properly with your lights turned on, then the problem is located in one of the circuits you turned off. Since it occurs when the car is moving, I would suspect that there's a wire in one of those circuits that's rubbing on a metal part. The rubbing has worn away the insulation so that now, when the car moves the right way, the bare wire is touching the body metal and grounding out. You can do a circuit-by-circuit trial where you turn one accessory on at a time for a while until you find the problem one, or you can examine every wire you can find, looking for a contact point. There's a good chance you'll end up doing some of both. Once you find it, a wrap or two of electrical tape over the worn wire, maybe a patch of tape on the bare metal, and rearranging the wire a bit so it can't touch anymore, should eliminate the problem. I think I'd start looking under or behind your dashboard, maybe from the fuse panel to wherever each wire goes.