Remove Key, Radio Stays On? Help!

2001 Mazda Tribute
Came home from a vacation (in a different car) and neighbors said my Trib's radio had been playing the whole weekend we were gone. I checked but battery was completely dead...wouldn't even jump start. Bought new battery and started up. Removed key and radio was off. Went back out to car an hour later and the radio was on. Then I manually pushed the power button on the radio to turn it off, but the faceplate was still lit-up showing time. Put key in, turned to Accessory position then off again.. radio light went off. Again a while later the radio light was on again. Finally after a while of this back and forth, the power to the radio faceplate light would not turn off at all. I figured it wouldn't use much power...WRONG. Battery dead next day. Jumped battery and removed 5 amp fuse for radio. 2-days later battery dead again. There must be a lot of hidden things using power.. computers etc.. that are not getting shut off. Changed the ignition switch... didn't help. Changed the Accessory Delay Relay switch... didn't help. Arghh...what now??