Johnthen there is something else wrong with it,possibly a bad connection,or the alternator isn't charging enough on it,you need to have it checked at a shop,you cant drive it like this,if its not charging,it ill kill the new battery in it in no time,take it and have it checked,good luck on it.while car is running with headlights on pull the positive side terminal on the battery....if it dies......bad alternator or very loose belt. loose belts usually squeak alot. I have seen a wire come loose once at the connector of alternator for one wire goes to the sensor light on the dash panel this wire was the smallest size and yellow on a ford. also look at the connector too for black burn marks meaning bad connection.
If the alternator is like 300 bucks at autozone....then hit the junk yards....offer them 30 bucks.take car to any parts place they will do free diagnostic on charging system free and i think your alternator is badThe battery light will stay when your alternator is bad.