Windstar 2001 Electrical Problem

The symptoms I'm having are thus: As I was driving, the peripheral accessories began to fail, radio, lights etc. Then the gauges went to zero. Th engine began to rev and die rev and die. I coaxed the vehicle home where I ended with a dead battery. I've replaced the old battery (which was pretty old anyway) with a new fully charged one. I was letting the vehicle warm up last night when the same symptoms appeared. I'm not a handy mechanic but am capable enough if pushed in the right direction.. I've heard anythign from bad alternator to a computer chip. Any ideas?