The 1st pic looks like an aftermarket circuit/wire, at least the spade connector end is, maybe its to a starter kill or anti-theft type device? The 2nd pic of the dark blue/yellow stripe wire under the hood right by the a/c compressor is for the a/c compressor clutch, it shouldn't have anything to do with the starting problem.
edit: after reading your post again, are you saying the wire you found inside on pic #1 goes under the hood to the wire in pic #2? If so a previous owner might have the a/c switch bypassed to another switch somewhere on the dash, either to turn it on or off when selected.
I don't know what you are trying to show with the last set of pics but if you were looking for the starter wire leaving the ignition switch, its the yellow/ dark blue stripe. The 5th and 8th pic shows the ign switch connector and the yellow/dk blue wire is hidden right behind the taped harness going to the smaller connector.