If I'm reading your question correctly, you don't need to use Zone2. Zone2 is for adding an extra set of speakers in another location altogether, such as in another room.
It sounds to me like all you want to do is, as you state, "play two different sources at once". You simply would like to show a DVD which has no soundtrack, while you play the radio.
Correct?
With your receiver, you can definitely monitor one video source (in your case, DVD player) and a different audio source (in your case, radio).
Use the "
Video Select" button and function knob on the front of the receiver.
From the lower left corner of pg. 67 in the 3805's owners manual:
http://www.usa.denon.com/AVR3805_DFU_ownersmanual.pdf
Your remote may or may not allow you to perform this function, but it could possibly be able to be programmed to do so; I'm not certain about your particular remote.