You've got a bad cable or connection somewhere. Take all the connections apart and double check them. I can almost guarantee it's not a component problem.
Get someone to turn the key while you watch the cables, you'll likely see or hear the problem.
Another test, hook a jumper cable from your battery negative post to a bolt on the engine and try it again. If it goes you negative cable is bad.
If your battery cables have those clamp-on replacement ends, throw the cables in the garbage and go buy new. When those ends are installed it opens the cable up to moisture and corrosion. I've cut the insulation off of cables and found them green from one end to the other.