2004 Dodge Durango, 5.7 hemi 4X4 Electrical Problem

Hello, this is my first question. My battery is completely discharging overnight. Totally dead. I have checked the new battery (2mos. old) and have concluded it is not a battery issue. A 10 hour slow charge, with cables disconnected, will return battery to full charge and starting and all other functions appear to be normal as long as engine is running. I did however notice that on shutdown it sounded like the CD player was cycling while the key was off. I manually turned it off but there still seemed to be power to the radio? After the sounds quit I left the vehicle overnight and by morning it was stone dead again. If battery cable is disconnected overnight then reconnected it starts. My problem is where do I start to look for the problem? Has anyone had a similar problem? Any help would be appreciated as you can imagine how frustrating it is to have to disconnect on every engine shutdown.