Here's a horror story that sounds much like the problem discussed here.
I have been having a problem with slow cranking at the starter after a couple hours of driving and with the battery going dead if the car is unused for a few days. Sometimes the car would start after an hour's rest, sometimes it would not. Sometimes it would start with a jump, sometimes it would not. The alternator tested good at many, many tests, so I have not yet replaced it. I will have to replace it, since it is the ONLY thing that is not new. I have replaced the starter, the battery, the ignition switch, the neutral safety switch and today, after giving up on doing it piece by piece I finished installing a brand new wiring harness, which took a few days. I changed the battery, started the goddang thing and let it run for almost an hour, shut it off and to my dismay, the problem persisted: at the second try the starter would crank really slow, then start clicking. No start. Before I plop down more money to replace the alternator I registered here to see if I could find some advice. The testlight method suggested above sounds really practical, I shall run it tomorrow.
Also, the alternator has R and F terminals, besides battery and ground. I connected it the way my new harness said, with a brown wire left hanging, as it was before. The R terminal is not plugged to anything. A red wire from the battery went to the F terminal. I did this without fully comprehending the function of the terminals, and the charging system tested good on my tester.
Any advice at all will be greatly appreciated, I'm confident that if I will find the answer to that really annoying bug it will be in these forums.