The parts are all fine, but a new battery is draining, so there has to be a short to ground somewhere. To find out where the short is all you need is a simple 12 volt test light (You can find them for as little as $5 online)
Here's a YouTube vid showing how to track down where the short is.
It could be something as simple as a wire that has been rubbing against something since the car was new and finally wore through and is now making contact with the body somewhere.
Keep us posted on your progress!
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