I ran into something similar to yours. Traced it to the battery cables, then the grounding bolt from the fuse box. The grounding bolt was lose, so if it was sitting right my car would start. Other times would not. If I shook the cables it would start then sometimes not. Replaced the battery terminal clamps and worked for a few days then not. Then noticed the bolt just barely screwed to the chassis. Tightened it down to 5 ft/lbs and no problems since.