I would start by checking the connections on the back of the ammeter gauge. All of the power goes through there except, of course, for the power that goes directly to the starter. Put the power to the ignition switch and the dome light and everything else does. Sometimes they're not loosen up on the studs on the back of the gauge and cause problems similar to what you are having.
Not likely the cause IF using a pushbutton on the relay...
Good point. If he's using the remote button, and it is connected directly to the battery.
If that is the case, then I agree that the battery cables and battery cable connections are the best place to start.
