Well, the starter is NOT fused, that's why there may be smoke there, otherwise the fuse would have just blown. You can pull all of the fuses, and it will probably still smoke. I would suggest finding the starter motor, and making sure that it is someplace that looks like your smike could have come from. I would disconnect the cable that leads from the battery to the starter at the starter end (and make sure that the end doesn't touch anything). Then hook up the battery and see if the smoke is there.

PS, why are you doing all of this work on your neighbor's car. Is it a really good deal? After you get it fixed is he going to raise the price??

First of all, thanks. I was curious about the polarity initially as well, because it appeared that the red cable was on the negative terminal. Not the case. The battery was merely reversed from the one in my other car which I was using temporarily just to try cranking it. But I switched the cables just to see. I never inserted the key in the ignition either time, and smoke appeared within 3 -5 seconds both times. I do suspect the solenoid or starter. I am going to pull every fuse and reinsert them one at a time until I get smoke again to try to narrow it down. Is this a reasonable approach?