I'm trying to help a buddy of mine out with his 2002 Ram 1500 4x4 w/ 4.7L V8. It has a brand new battery and according to the tester at an Auto Parts store the charging system is working correctly. If I leave the vehicle for more than 24 hours without cranking it up the battery will die. So, it appears something is pulling power from the battery while the truck is off. I did figure this much out. When you turn the ignition off, the radio stays on. No biggy, it is suppose to cut off when you open the door, but it doesn't. I checked it 30 mins after I shut it off and opened then closed the door and the radio was still on. For a simple temporary solution I turned off the radio by the button on the dash and also turned off all interior lights from the control panel just to be on the safe side. 24 hours later the truck was still dead. The only light showing at all on the dash is the little red Anti-theft light. I'm pretty sure there is a sensor somewhere that has gone bad, but what else could be drawing the power like this? Thanks,

 

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Do you have any aftermarket accessories installed? such as alarms, or lights, or anything extra wired up that could be pulling power because it's not switched off. Some of the 12volt cigarette lighters are hot at all times, so make sure it's just not a radar detector or cell phone charger that's plugged in draining the battery.
Besides the very simple things to check... you mentioned that the radio remained on long after the truck was turned off, that might be due to a malfunctioning ignition switch. Do a search for ignition switches to see if any other symptoms match what you have.
Keep us posted.

There's also another type of test called an ignition or battery draw off test (or something like that) You need a meter that can monitor the amperage coming off the battery. One by one you pull a fuse to find the circuit that is drawing the most power.

 

Nothing aftermarket or plugged in. I'm going to try the ignition battery test thinging pulling out the fuses one by one. Good idea, thanks.

 

Good luck and I hope you find out what the problem is.
On a side note, I have a digital multimeter but I've never had luck with it on the amperage setting. I use it for volts and resistance that's it. The one time I tried to measure amps I had a nice show of sparks for a second and that lovely electrical "o-zone" smell lol. if only I remember where I put the manual for that thing . . .

 

Could be the ignition switch? Try jiggling the key around before you take out of the ignition to see if the radio turns off. I had this happen on my tuck not long ago. The fan and radio would stay on unless I wiggled the key around after turning the truck off.