Hi Grace,
This happened on my wifes 1994 Escort and it really baffled me because when an altenator normally goes the battery light comes on when the engine is running which indicates a low voltage output because part of the rectifier circuit normally goes open circuit and only half wave rctifies. But there was a short in the (rectifier) output stage of the altenator which was drawing current when the ignition was switched off which also caused the battery light to remain on even with the key out. it was dragging the battery votage right down too. I was lucky enough to have a good spare battery which i connected and the same thing happened. I was beginning to suspect a real major electrical fault because i have not seen an altenartor do this before but I replaced the alternator and it solved the problem. It wasn't a difficult job and it took me about an hour to do. If you take in your old unit to a motor factor or ford you can trade the old one in for a reconditioned unit - mine was about �55 with 12 months warranty. It sounds like the same fault to me and most people told me it wasn't the alternator - even a garage employee. I wish you luck and it would be nice to know how you get on.
Jason