Charging issues

I have intermittent charging issues on my 99 eldorado XTC. Twice in three months I have found the battery completely dead for no reason. With a jump it started quickly, ran fine and next stop, no dead battery. Today though driving down the road the computer told me the battery was not charging, and by the time I got home the windows would barely roll up, and after shut off, it would not turn over at all. Just for giggle, I jumped it 15 minutes later and voila, all was well, the car was getting 13.6 volts to the battery, all systems were go (during the problem the computer insisted my airbag, traction control, and ABS all needed servicing and the transmission was bumping into every gear) and the car drove great, like normal, and after shutoff it started like it was new. My quesiton is where do I start on diagnosis -= the generator, alternator, regulator, computer, battery?