Crank, click, then out!

There's a bad connection in one of the cables. You can find it with a test light. Turn the head lights on so current is trying to flow. Start with the probe and ground clip right on the battery posts. Move the probe to the battery cable clamp, then do the same with the clip. Move the clip to the body, then to the engine block. Next, move the probe from the positive cable clamp to the next place down the line which will most likely be the starter. You're looking for the first place where the test light doesn't light up. That's the point of the loose or dirty connection.