My battery won't recharge

Even a new alternator can be bad from the get go. Make sure your belts are good and tight(to specs). If the battery is discharging then the system is failing to send the proper (trickle) back to the battery. Have the new alternator checked and see if its bad as well. They say this can have something to do with the magnetic field the alternator produces and it or the diode can go bad in no time flat. Hope this helps.