I would start by checking the main lines from the battery to their respective locations for good continuity. Make sure the battery terminals are tight and clean, make sure the connections to the chassis ground, engine ground are good, tight, clean, as well as the connections to the power distribution box, starter, alternator etc.
It sounds like you have a bad connection, and this has happened to me in the past by not tightening the connections to the battery. The only time it did it was if I was not going to tighten it due to removing the battery from the vehicle right after using it to start it. I would go out and twist the loose terminal and voila.
Hoppy