Sounds like you have a bad connection somewhere, could be on either positive or negative side. Check all your battery cables for loose connections and corrosion and clean all connection points with a wire brush or sandpaper so they have a nice clean metal on metal contact. You might also have cables that need to be replaced. If the cables are all original, It wouldn't be a bad idea to just replace them all anyway.
I had a similar problem and after cleaning all connections replacing some parts, I found it to be the positive battery cable. Even though I cleaned and re-stripped the wire and everything , there was corrosion inside the cable about an or 2 up cable. Cut it off re-stripped and hooked everything up, problem solved.