The fuse box on top of the battery melts and shorts out the alternator wire/fuse. However, your method of removing the battery cable or alternator and letting the car run is a very bad idea, it's a quick way to short out electrical components.
If you suspect that the charging system is not doing it's job, the cable/fuse closest to the passenger side (large black cable) is for the alternator. You may test the fuse (I believe its a 200amp fuse) and you should do a voltage drop test from the cable on the fuse-box to the alternator, you shouldn't see a voltage drop of more than 0.2volts.
Another quick way to tell if the fusebox has overheated is to just look at it, sometimes you'll see the plastic melted around the green 30 amp fuses.
If you have anymore questions, let me know!
Thursday, March 28th, 2013 AT 11:06 PM