I had a similar problem that I fixed this weekend. Everything would visually and electrically check out except every now and then when going to start it you would only hear 1 click then nothing but interior lights. What I found was the positive cable that has 3 wires going to it, the one going to the starter had corrosion running down under the insulation quite a ways towards the starter. Replaced the end with a new connector while removing the section of corroded wire and all is good so far.