New batter but battery light stays on

You have a battery drain that should be diagnosed by:

Have a parts store test your alternator diodes; if OK then
Put an amp meter between battery ground and battery neg cable to read draw with key off, then remove one fuse at a time to find which one makes draw go away. Once you know which circuit is faulty, check all items on that circuit.

Some of the usual culprits are glove box door not shutting properly and making light stay on. Light in trunk staying on. Brake lights staying on because switch is misadjusted.

you will have to check else where as fuses do not stay on. They are simply a piece of resistance wire designed to burn out at a set current flow . So a 20 amp fuse will burn out at 21 amps. Look for relays or bulbs that are still on, like boot lights , glove box lights , interior lights etc

if the light stays on it could be a parisitic lose this is something that is drawing power from the batter but not fast anuff to kill it over night it may take up to three months but every time you drive it the altenater brings the power in batter back up so it will not die

I have a similar problem, intermitently the car will not crank. The dome light stays on which eliminates the battery. The clock on the radio turns off when I try to start it. Th Theft light is solid red the first time I try to start it, then latter after a few tries the red light is off, but it still wont start. I tried moving the shifter when in park, I even tried starting it in neutral. After a while it starts and once started it runs fine. I will have to take it to Ford next week. We just do not want to drive it, it is too unreliable. It is a 2000 Ford Taurus.

When this happens, are the gauges dropping or not working properly or at all? Check the alternator. May not be charging so everything is running off the battery. The battery is used mostly for starting, but the alternator recharges the battery, so if after driving for a short while, and alternator not charging, everything electrical will drain the battery. You can sometimes drive the car for a while when this happens, or if the alternator goes out completely, the car will not run at all.

Check the exterior bed light to see if it is staying on but has a blown bulb. Also, you want to check the wiring on any devices you may have installed after you bought the truck to include alarms for shorts. If you had an alarm installed it is probably the alarm that is the problem.

Altinator is faulty.

if you have no ignition lights on your dash, no reverse lights and if when you start the car up the battery light stays on your ignition fuse has blown controlling these items. change the fuse. not sure if it is your ignition lights by your posting. if it is not please give a more detailed report,try to help if i can. hope this helps.

This is caused by the Alternator. Also, Check the Belt for Tightness.

brake light switch or a headlight switch