1995 Chrysler Le Baron 95 GTC 3.0L No electrical power (at

Hello fellows,
My 95 GTC has had much attention lately, owing to the fact that it is about to become the property of my 16 yr old.
My (our) problem stems from that thin (br/wh) wire that's been hanging out of the wiring harness next to the battery since the car was new. It's never had a use that I can remember. What is that wire for?
Details follow: The wire wound up on my + bat terminal. The plastic connector "thing" has broken off on mine, leaving a bare end to that wire.
Lately when I was attempting to move the car in my driveway, when I threw the key to "start" all went dark! Pulling the key out completely, and carefully throwing it to "run" all the dash lights came on properly the second time, so I threw it to start again and all went black again. I heard clicking coming from the module behind the passenger side floor. So I quickly jumped out to pull the neg bat terminal.
Opening the hood revealed that br/wh wire laying on the top of the + bat terminal, not cooked. Any further attempt to manipulate the system has resulted in a steadily declining evidence of power anywhere in the car, and a fully charged battery, showing no sign of stress. (Fusible link gone bad perhaps?)
I'll post with my progress. Any help would be appreciated.
Karl