I just went through that problem with a friend's '97 Ford Tarus......
It was practically everything. Battery, alt and starter were all bad.......took them off one by one and had them bench testedand replaced in an elimination process. Everytime, the word was....."No Good." My normal advice would be to check at the relay by jumpering it. The Tarus couldn't, as they use one of those cubes (relay was it #86 or #87? anyway).......not like the old Explorer uses. And, not to mention that the power relay box cover was for another vehicle and the owner's manual is S*#!.
You could save some time by removing and taking both the battery and alt down to be bench tested at the same time.
Good luck.
Aloha, Mark