Battery not charging

Your battery sounds like it's on a constant draw from a circuit that is not working properly. For the test light between your battery and your positive cable. With your key in the off position. also check and see if you have a circuit that still has power going to it by checking each of your fuses to ground if you have a stuck relay and you remove the fuse .. by putting your test light back in place it should not light if you've eliminated the draw on your battery..

You may also want to check your fusible links they are not fuses in your fuse box but are wires that are actual fuses there is one going to your alternator for the charging circuit and if one of those fuses are bad it's not going to allow your alternator to charge. your alternator should put out between 12 and 16 volts depending on how low your battery is and the amount of draw but if your alternator is not putting out anything it could be one of those fusible links.